Microeconomics – Problem set 4
Ex. 1
Let’s return again to the production function 𝑄 = 50𝐿1
2𝐾1
2 that we introduced in exercise 2,
problem set 3.
a) How does minimized total cost depend on the output Q and the input prices w and r for this
production function?
b) What is the graph of the long-run total cost curve when w = 25 and r = 100?
c) What are the long-run average and marginal cost curves associated with this long-run total
cost curve?
Ex. 2
In a competitive market a firm faces a total cost of production given by CT = 4q2 + 12q + 36.
The market price is p=28.
1) Derive the functions of the fixed cost, the variable cost, the average variable cost, the
average total cost and the marginal cost.
2) Find the optimal quantity the firm will produce in the short run and calculate its profit
3) Derive the firm’s short-run supply curve.
4) Assume that 8000 firms are operating in this market, each with the same cost function.
What is the market supply function in the short run? If the demand function is Qd =
12000 – 200p find the equilibrium price and quantity in this market.
5) Find the long-run equilibrium for the firm. Assuming the same demand function as
above, find the market equilibrium price and quantity as well as the number of firms
operating in the market.
6) Provide a graphical representation
Section 2: True, false or uncertain
Decide whether the following statements are TRUE, FALSE or UNCERTAIN (i.e. they are true only under
specific hypothesis not contained in the statement). Justify the answer. [The justification is more important than the
initial answer being true, false or uncertain]
1) Suppose that all the firms active in the competitive market for carrots are identical and
that their long-run average cost curve (ACLR) is as depicted in the figure below (where 𝑞i
is the quantity of carrots produced by firm 𝑖). Aggregate demand for carrots is Qd =
