ECON 1100 Intermediate Microeconomics Assignment #4

ECON 1100: Intermediate Microeconomics Assignment #4 

 

1. Homer is a deeply committed lover of chocolate. Assume his preferences are Cobb-Douglas

over chocolate bars (denoted by C on the x-axis) and a numeraire good (note: we use the notion of a numeraire good to represent spending on all other consumption goods – in this example, that means everything other than chocolate bars – its price is always $1). a. Homer earns a salary that provides him a monthly income of $360. Last month, when the

price of a chocolate bar was $4, he bought 45 chocolate bars. Using what we know about

the relationship between the parameters of the Cobb-Douglass utility function and

expenditure shares, write down the specific utility function for Homer (i.e. put in the

appropriate numbers for ???? and 1 − ????).

b. Use your answer to part (a) to derive Homer’s Marshallian Demand for chocolate bars, his

Compensated (Hicksian) Demand for chocolate bars, his Compensated (Hicksian) Demand

for the numeraire good, and his expenditure function. Show your work for full credit!

c. Imagine the mayor of the city in which Homer lives sees Homer as representative of the

voting public. He is worried about being reelected, given that citizens like Homer are about

to be made unhappy by his new regulation on chocolate bar producers, which will increase

the market price of chocolate bars from $4 to $ 9. Use the implied change in the

Expenditure Function to compute Homer’s Compensating Variation for this potential price

increase, that is the amount that Homer would need to be paid to maintain his original

utility given the new price for chocolate bars.

d. Draw a rough graph of the Marshallian Demand and show the loss of Consumer Surplus that

would be associated with this price increase? Set up the integral that you would use to

calculate the loss (no need to actually solve for the area).

e. Now redraw your graph from part (d) and add the Compensated Demand function for

chocolate bars. Denote both CV and ?CS on the graph Identify the difference between CV

and ?CS and clearly label it.

f. Briefly provide intuition, using the Slutsky equation, for why CV and ?CS diverge. What

factors cause the divergence between CV and ?CS to be large or small? Make sure your

answer is no longer than 3 sentences.

2. Consider the production function ???? = ???? 1 3????

2 3. Let r and w denote the prices of K (capital) and L

(labor). Suppose ??? = 27 (fixed) and L is variable.

a. Write down the expression for the short-run production function.

b. Compute the marginal product of labor (????????????) and the average product of labor (????????????). Is

the ???????????? increasing or decreasing? Is ???????????? >, <, or = ?????????????

c. Find expressions for fixed cost [F], variable cost [VC(q)], average cost [AC(q)] and

marginal cost [MC(q)].

d. Find the production efficient level of output (q*) where unit costs (AC) are cheapest

(minimized), your answer will depend on w and r.

e. If a $15 specific tax per unit is imposed, what are the new cost functions (FC, VC, AC and

MC)?

 

 

3. Consider a typical short-run production scenario for a firm.

a. Graph the MPL and APL. Assume that at low levels of production MPL > APL. Explain the

shape of the APL.

b. Graph AFC, AVC, AC & MC. Explain why MC crosses AVC & AC where it does.

c. Graph ???? = ????(????, ???). How can we identify MPL and APL on the graph? Show the point

where APL is at its maximum.