Download Economic Analysis of Sugar Market and Electricity Market and more Exercises Marketing in PDF only on Docsity!
SOLUTIONS TO HOMEWORK SET
a. In this problem, we have two different supply functions (domestic producers and foreign producers) and one demand function. To find the equilibrium we need to combine both supply functions into one “effective” supply and find its intersection with the demand. Let’s construct the “effective” supply function: Think of the supply function as the minimum price that a producer is asking to deliver a given quantity of sugar. From Figure 1, we can observe that are some US producers that are willing to deliver sugar for less than 10 cents/lb. (the world price). There are also US producers that are asking for a price higher than 10 cents/lb. However, given that US consumers can purchase sugar from foreign producers at 10 cents/lb, they will not be interested in this relatively expensive US domestic supply. Therefore, our “effective” supply will be formed by those US producers willing to sell sugar for less than 10 cents/lb and for foreign producers selling at 10 cents/lb. The “effective” supply is the bold line in Figure 1.
90
10
10 53. Quantity (billion lb)
Price (US$ cents/lb)
US Demand^ US Domestic Supply
World Price
Figure 1 – Sugar market under free trade.
At this point, it should be clear that the equilibrium price will be equal to the world price of US$ 10 cents/lb. At this price, the domestic demand will be: Q = 60 – 2 / 3 10 = 53.3 billion lb. The quantity supplied domestically will be: Q = P = 10 billion lb. Imports under free trade will be: 53.3-10 = 43.3 billion lb.
The consumer surplus will be ½(90-10)53.3 = 2,133.
Be aware of the units: you are multiplying (US$ cents/lb) (billion lb) = billion
US$ cents! ⇒ You have to divide the result by 100 to have US$ billion
Thus, the consumer surplus will be US$ 21.33 billion. The producer surplus will be ½ 10 10 = 50. Then, the producer surplus will be US$ 0.5 billion
b. In this scenario, the world price is not relevant (there are no imports), so the US demand should be equal to the US domestic supply:
Qd^ = Qs 60 – 2 / 3 P = P P = 60 3/5 = 36 cents/lb Q = 36 billion lb.
Without imports, the quantity demanded will be 36 billion lb. and the equilibrium price will be 36 cents/lb
90
10
36
10 36 53. Quantity (billion lb)
Price (US$ cents/lb)
US Demand^ US Domestic Supply
World Price
Figure 2 – Sugar market without imports
The equilibrium price will return to the world price of 10 cents/lb. At this price, the quantity demanded will be 53.3 billion lb. The domestic supply is now benefiting from the subsidy, so Q = P+15 = 10+15 = 25 billion lb. Imports will be 53.3 – 25 = 28.3 billion lb.
The consumer surplus will be ½ (90-10) 53.3 = 2,133 billion cents ⇒ US$ 21.33 billion. (Note that this is the same result as part a.) The producer surplus (A+B+C) will be ½ (10+15) 25 = 312.5 billion cents ⇒ US$ 3.125 billion The amount of the subsidy is 15 25 = 375 billion cents ⇒US$ 3.75 billion
Figure 3 shows the amount paid by the government as a subsidy (B+C+D):
Subsidy
B and C are transfers from the government to producers and increase producer surplus compared to the result in part a. The government also pays D as part of the subsidy. However, this transfer is not part of producer surplus because it only offsets the additional costs of domestic producer compared with foreign producers.
The deadweight loss in this situation corresponds to the amount paid by the government that is not transferred to producers, but covers additional costs of producers that are less efficient than world producers. The deadweight loss is equal to the area of D = ½ (25-10)(25-10)= 112.5 billion cents = US$ 1. billion.
We arrive at the same result if we compare the total surplus of the part a. (21.33+0.5) and the total surplus of part c.(21.33+3.125-3.75). The difference is US$ 1.125 billion.
d. We can compare the situation under the three previous scenarios:
(in US$ million) Free Trade No Trade Subsidy Consumer Surplus 21,333 9,720 21, Producer Surplus 500 6,480 3, Government -- -3, Total Welfare 21,833 16,200 20, Clearly, consumers are much better with free trade than without it. Therefore, consumer organizations, such as soft drink manufacturers and candy makers will lobby in favor of free trade in sugar. Producers benefit from trade barriers or subsidies and, in consequence, will lobby in order to obtain such privileges.
e. Let Q equal the total quantity supplied of sugar and q equal the quota that the government should set in order to have a domestic production of 25 billion lb. The total quantity traded in the market (Q) will come from imports (q) or from domestic production (25 billion lb), so we can formulate the following relationship for equilibrium: Q = q + 25 … (I)
Also, in Figure 4 we can observe that the market will have a kinked supply curve where: Q = P if P < 10 cents/lb = P + q if P >10 cents/lb
Solving for P and substituting for Q using (I): P = Q – q = 25 cents/lb
Using this price in the demand equation, the total quantity demanded in equilibrium will be: Q = 60 – 2 / 3 25 = 43.3 billion lb. The quota will be 43.3 – 25 = 18.3 billion lb.
igure 4 – ugar market ort
e will use Figure 4 to describe the consumer and producer surplus. The onsumer surplus is the area of the triangle E = ½(90-25)43.33 = 1,408.
lion cents = US$ 0.5 billion S$ 1.5 billion billion cents ⇒ $
F S with an imp quota
W
c billion cents ⇒ $14.08 billion The domestic producer surplus will be A+B+D: A: ½ 10 10 = 50 bil B: (25-10)10 = 150 billion cents = U
90
10
10 28.3 53.
25
Quantity (billion lb)
Price (US$ cents/lb)
(^) US Domestic Supply + Quota
Q
US Demand US Domestic Supply
World Price A q
B C D
E
D: ½(43.3-28.3)(25-10) =½(15)(15) = 112.
1.125 billion
The “effective” supply is the bold line in Figure 5. The equilibrium will occur when supply equals demand: P=90 – 1.5Q, then: Q-25 = 90 -1.5Q Q = 46 billion lb. The quantity demanded is 46 billion lb, composed of 15 billion lb. of imported sugar, 10 billion lb. of HFCS and 11 billion lb. of domestic sugar production The market price is 46 – 25 = 21 cents/lb.
The surplus analysis is based on Figure 5. The consumer surplus is equal to A = ½ (90-21)46 = 1,587 billion cents = US$ 15.87 billion The domestic sugar producer surplus is equal to B+C+E+F+H Area B: ½ 10 10 = 50 billion cents Area C: (21-10) 10 = 110 billion cents Area E: ½ (15-10) (30-25) = 12.5 billion cents Area F: (21-15) (30-25) = 30 billion cents Area H: ½ (21-15)(46-40) = 18 billion cents Then, the domestic sugar producer surplus is 220.5 billion cents or US$ 2. billion
15
90
10
10 25 40
21
30 46 53.
Quantity (billion lb)
Price (US$ cents/lb)
US Domestic Supply + Quota + HFCS
US Demand^ US Domestic Supply
World Price
Quota HFCS
J^ K
G H^ I L M
F C^ D E B
A
Figure 5 - Sweetener Market with HFCS and Quotas
HFCS producer surplus is G = (21-15)(40-30) = 60 billion cents or US$ 0. billion World sugar producers surplus is D = (21-10)(25-10) = 165 billion cents or US$ 1.65 billion
The deadweight loss is I+J+K+L+M
Area I: ½ (21-15)(46-40) = 18 billion cents Area J: ½ (15-10) (30-25) = 12.5 billion cents Area K: (15-10)(40-30) = 50 billion cents Area L: (15-10)(46-40) = 30 billion cents Area M: ½ (21-10) (53.3-46) = 40.3 billion cents Then, the deadweight loss is 150.83 billion cents or US$ 1.5083 billion
- In order to understand the different statements, it is useful to summarize the information in the following table:
Units Revenue Variable Fixed Total Profit (P.Q) Cost Cost Cost from table given from table given VC+FC TR - TC 100 16,000 5,000 30,000 35,000 (19,000) 200 32,000 15,000 30,000 45,000 (13,000) 300 48,000 24,000 30,000 54,000 (6,000) 400 64,000 33,000 30,000 63,000 1, 500 80,000 43,000 30,000 73,000 7, 600 92,000 54,000 30,000 84,000 8, 700 104,000 67,000 30,000 97,000 7, 800 116,000 83,000 30,000 113,000 3, 900 128,000 103,000 30,000 133,000 (5,000) 1,000 140,000 128,000 30,000 158,000 (18,000)
After examining the table, we can conclude that the maximum profit is obtained producing 600 units. If the firm produces less, it is losing the opportunity of additional gains from selling up to 600 units. If the firm produces more than 600 units, the increase in costs due to the additional units will be higher than the revenue extracted from the additional units sold.
Let us look at two examples: i) Production of 500 units: it is not the optimal situation, because increasing from 500 to 600 means additional revenue of $12,000 with additional costs of only $11,. ii) Production of 700 units: it is not the optimal situation. Moving the production from 600 to 700 increases revenues by $12,000 and costs by $13,000. The result is a loss of $1,000 in the last 100 units. This idea of additional costs incurred when the number of units produced is increased is known as Marginal Cost. Its general formula is:
Marginal costs: MC = ∆ Total Costs (Q) / ∆ Q
a. To answer this question we will use some of the notions discussed in the answer to question 1. First, we have three producers and one demand function. To calculate the equilibrium price and quantity we will need to combine the three plants in an “effective” supply curve and find the intersection with the demand function. Second, it will be useful again to think of the supply function as the minimum price that a producer is asking to deliver a given quantity.
Taking into account the previous two statements we can proceed to construct the “effective” supply of electricity. The plant that will ask for the lowest price is the one with the lowest cost, i.e. the coal plant. After supplying 4. GW-h, this plant reaches its maximum capacity. To supply more electricity, it is required to choose between oil and gas. Once again, the lowest cost producer (i.e. the oil plant) enters before higher cost producers, until it reaches its maximum capacity. Only if the electricity required exceeds 6.6 GW-h, the gas plant will produce.
You can see the entire schedule in Figure 6
Figure 6 – Effective Electricity Supply in Cleanland
The special form of this supply curve forces us to adopt a different approach to solve the problem. We know that the price will take one of three values:
P = 1310 if Q ≤ 4. = 1730 if 4.6 < Q ≤ 6.6 (= 4.6+2.0) = 1860 if 6.6 < Q ≤ 9.3 (= 6.6+2.7)
4.6 6.
1310
1730
1860
Quantity (GW-h)
Price (C$/GW-h)
Coal
Oil
Gas
However, we do not know at which level the supply will intersect the demand. One way to find the equilibrium for each season is replacing each of the three values of P in the demand equation and check if the resulting Q belongs to the intervals presented above.
Dry Season: Q = 14.25 – 0.005P
If P = 1310, then Q should be less than 4.6. But, if we replace P in the demand equation ⇒ Q is 14.25- 0.0051310 = 7.7 > 4.6 (X) If P = 1730, then Q should take a value between 4.6 and 6.6. Replacing P in the demand equation ⇒ Q is 14.25- 0.0051730 = 5.6, which is in the range of Oil production ( 9 )
Then, the price for the dry season is C$ 1,730/GW-h and the peak demand is 5. GW-h. The consumer surplus will be ½ (2850-1730) 5.6 = C$ 3,136 during the peak hour The coal plant surplus will be (1730-1310)4.6 = C$ 1,932 during the peak hour The oil plant has no surplus (Marginal cost = Price). The gas plant does not produce
Wet Season: Q = 18.3 – 0.005P
If P = 1310, then Q should be less than 4.6. But, if we replace P in the demand equation ⇒ Q is 18.3 – 0.0051310 = 11.75 > 4.6 (X) If P = 1730, then Q should take a value between 4.6 and 6.6. Replacing P in the demand equation ⇒ Q is 18.3- 0.0051730 = 9.65 > 6.6 (X) If P = 1860, then Q should take a value between 6.6 and 9.3 ⇒ Q is 18.3- 0.0051860 = 9 < 9.3 ( 9 )
Then, the price for the wet season is C$1,860/GW-h and the peak demand is 9 GW-h. The consumer surplus will be ½ (3660-1860) 9 = C$ 8,100 during the peak hour The surplus of the coal plant will be (1860-1310)4.6 = C$ 2,530 during the peak hour The surplus of the oil plant will be (1860-1730)2 = C$ 260 during the peak hour. The gas plant has no surplus (Marginal cost = Price).
Consumers will have to pay a higher price for electricity during both the Dry season (1860 vs. 1730, a 7.5% increment) and the Wet season (2076 vs. 1860, a 11.6% increment). Coal plant increases its surplus because of the higher price paid by consumers. Gas plant has surplus during the Wet season (it was zero in the previous scenario), so it improves its results. Oil plant loses because now it does not have any surplus (it does not produce during the dry season and only covers its costs during the wet season). The previous evidence supports the idea that both the coal and gas plant will be in favor of the tax. On the other side, the oil plant and the consumers will oppose this measure.
a. The user cost of capital (UCC) of the “Daily Bugle” should change after the mayor’s decision, because the UCC reflects the best alternative use of the asset. The new regulation allows more uses of the Blue House, and the highest-valued alternative use will now be chosen from a larger set of options. The only case in which the user cost of capital will remain the same is if, after examining all the new alternatives, they decide that the best possible alternative use for the building did not change. b. The activists’ argument is wrong because they ignore opportunity cost. The fact that the Bugle pays no rent does not mean its costs are low. The opportunity cost of staying in the Blue House is the highest valued alternative use for the property. For example, say that the highest valued alternative use came from leasing the Blue House for other uses. These foregone lease payments should be incorporated into the cost of keeping the Bugle in the Blue House.
5. TRUE
When a firm experiences economies of scale, its average cost is decreasing with output. Economies of scale consider the average cost of production for the entire amount of output produced, whereas marginal cost considers only the last unit produced. If average cost is decreasing, then marginal cost must be below average costs, although marginal cost can still be increasing (see the graph on page 226 of the textbook).
