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ECON130 IC-BC model Assignment 01
Objective: To demonstrate you can use Excel to plot budget constraints and indifference curves, and use these to analyse the optimal choice of a consumer. Due date: 12:00pm (midday), Tue 10 Aug 2021. Submission: Submit your completed Excel workbook via the link per the Submission instructions. Do not submit as a PDF, DOCX or other file format. Instructions: Read the information below first. Then use the Excel file supplied to complete the questions (see page 3). 1 Download a copy of the Assignment Excel file from Blackboard. Name your Excel file with your Student ID number. E.g. 300123456.xlsx. Do not name it anything else. Open the Excel file. Write your name (in cell B1) and select your Student ID number from the dropdown list (cell J1). Your assignment is based on your ID number so check that you have selected your Student ID number. Contact [email protected] without delay if you cannot find, or have a problem entering, your ID number. For answers requiring a numeric answer, you should include your calculation (i.e. your formula) in the relevant cell of the Excel file. This constitutes your working for the question, and will be marked. If your calculation is incorrect due to a minor error in the formula - which can be identified from your working - consistency marks may be awarded. Save and submit your completed assignment via the link on the course Blackboard.
Budget constraint Suppose c 1 and c 2 represent the quantities of two goods that an individual consumes, p 1 and p 2 represent the prices of the two goods, and M is the consumer’s income. A consumer’s budget constraint may be stated as: p 1 c 1 + p 2 c 2 = M. To plot the budget constraint in (c 1 , c 2 ) space, the budget constraint equation needs to be rearranged so it is in the form c 2 = F (c 1 ,... ). 2 This equation calculates c 2 (the variable on the y-axis) for a given value of c 1 (the variable on the x-axis), and fixed values of M, p (^1) and p 2. The given value of c 1 and corresponding value of c 2 are a pair of (x,y) coordinates that can be used to plot a specific point on a budget line. Below, the budget constraint is re-arranged to give an equation for a budget line. p 1 c 1 + p 2 c 2 = M (1) ⇒ p 2 c 2 = M − p 1 c 1 (2)
⇒ c 2 =
M − p 1 c (^1) p (^2)
Recall that the equation for a straight line may be written as: Y = a + bX, where a is the value of the intercept and b is the value of the slope. In the case of the budget line above, a = M p 2 and b = − p p^1 . (^1) If you do not have a computer that has Excel, you should complete this assignment using a computer on campus at the University that does. If you attempt to use another programme and there is a problem, your assignment will be given a mark of zero, and resubmission after the due date will not be permitted. (^2) I.e. the budget constraint equation is rearranged from the form M = F (c 1 , c 2 , p 1 , p 2 ) to the budget line equation in the form c 2 = F (c 1 ,... ).
Utility function
A utility function may be represented by an equation of the form: U = d(a
c 1 + b
c 2 ), where a, b and d are parameters. (Different numeric values of these parameters may be used distinguish one person/set of preferences from another.)
For example, if a = b = 4 and d = 0.5, the utility function is: U = 0.5(4√c 1 + 4√c 2 ).
Indifference curve
Similar to the budget constraint, the utility function can be rearranged as follows to give the equation for an indifference curve (for a given level of utility, Un ).
Un = d(a
c 1 + b
c 2 ) (4)
⇒
Un d
= (a
c 1 + b
c 2 ) (5)
⇒
Un d
− a
c 1 = b
c 2 (6)
⇒
b
Un d
− a
c (^1)
c 2 (7)
⇒c 2 =
b
Un d
− a
c (^1)
Note that the indifference curve calculates a value of c 2 for a given value of c 1 that yields the given level of utility (Un ).
For example, if a = b = 4, d = 0.5 and Un = 20 then the equation for the indifference curve is: c 2 =
4
c (^1)
⇒ c 2 = (10 −
c 1 ) 2.
Note: The assignment questions are on the following page.