October 24, 2000
Question One (20 marks)
Jennifer's preferences for hot sandwiches and cold sandwiches can be represented by U(h,c) = c4h. Prices of hot sandwiches and cold sandwiches are represented by ph and pc. Jennifer's weekly lunch income is m.
A) (5 marks) Find Jennifer's weekly demand for hot sandwiches.
MRS=- MUc/MUh=-4h/c. (2 marks)
Optimality condition: MRS=- pc/ph. --> -4h/c=pc/ph. (1 mark) Substituting this expression into the budget constraint pcc+phh=m, you will find: c=4/5*m/pc, h=1/5*m/ph. (2 marks)
B)(5 marks) Jennifer works in an office building with 399 other people who each have the same preferences and lunch income as Jennifer. What is the market demand function for this group of 400 individuals?
Aggregate demand=400* 1/5*m/ph.
C)(5 marks) When each person's m = $30, and when ph = $4, what will the total number of hot sandwiches demanded be?
D) (5 marks) Find the price elasticity of demand for hot sandwiches when ph = $4 and each person's m = $30.
Elasticity=- h/ ph* ph/h (note: do not be too keen about the minus sign) (3 marks) h/ ph=-1/5*m/2ph 2=-D/ ph. (1 mark)
Therefore, the elasticity=1 regardless of the price. (1 mark)
Question Two (25 marks)
Weedham School has no computers and no printers and no money to buy any. Computers cost $1000 each and printers cost $200 each.
A) (2 marks) Mr. Gates announces that he will send 10 new computers and 10 new printers to the school. The school can keep this equipment or sell it as new at the prices given above. What is the value of this endowment?
B) (10 marks) Weedham School's demand for printers is x = m/2px, where m is the value of the endowment and px is the price of printers.
Based on the information given so far, how many printers does Weedham School demand? Will the school be a net buyer or a net seller of printers?
m=12000. px=200. Therefore, demand=12000/(2*200)=30.
Initially the school has 10 printers, so he will be a net buyer.
C) (3 marks) Are printers a normal good for Weedham School?
The demand is increasing in income m. Therefore, it is normal good.
D) (10 marks) Weedham School reconsiders its plans when the price of printers suddenly increases. Without doing any math, discuss the substitution effect, income effect, and endowment income effect of this price change. What will be the total effect of this price change on the school's demand for printers?
First, we treat m given and see substitution and income effect.. 1.The substitution effect: effect of price change with adjusted income=initial income +(previous demand)*(price change). Normally, income compensation by adjusted income is not high enough, so that the price increase leads to decline the demand. (3 points) 2.The income effect: effect of income change by initial income - adjusted income