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Unformatted text preview: 1 Commerce 295: Sections 101-103 FRE 295: Sections 001 and 002 Fall 2010 Assignment 1 Assigned: Sept. 23/Sept. 24 Due: Oct. 7/8 Each question is worth 20 pts. Question 1: Supply and Demand A competitive consulting industry consists of 20 consultants, each with a supply schedule q S = - 4 + 2p. The variable q S is the number of hours that the consultant works each week and p is the consultants hourly fee. Market demand for consulting services is given by Q D = 1000 50p. a) Derive an expression for the market supply schedule for consulting services and graph it together with the market demand schedule (Hint: Market supply is just 20 times individual supply.) When constructing your graph allow the horizontal (quantity) axis values to range from 0 to 1200 in increments of 100 and the vertical (price) axis values to range from 0 to 30 in increments of 5. Please carefully label your graph and draw it to scale as best you can. Show the equilibrium point on the graph. (3 pts) Market supply is given by: 20 S S Q q = . Substitute in 4 2 S q P = + to obtain 80 40 S Q P = + . To graph this schedule invert it to obtain: 2 (1/ 40) S P Q = + . To graph the market demand schedule invert 1000 50 d Q P = to obtain 20 (1/50) d P Q = . 1000 Q 400 12 16 D (slope is -1/50) S (slope is 1/40) 2 Equilibrium point b) Use algebra to calculate the equilibrium price and quantity of consulting services. (3 pts) Set market supply, 80 40 S Q P = + , equal to market demand, 1000 50 d Q P = , and solve for the equilibrium price: * 12 P = . Now substitute this equilibrium price into either 80 40 S Q P = + or 1000 50 d Q P = to obtain equilibrium quantity * 400 Q = . 2 c) The government has decided to tax consultants $5 for every hour of consulting service that they provide. Draw a new graph and show how the tax affects the equilibrium prices for both buyers and sellers. Also show how the equilibrium quantity is affected. (4 pts) The $5/hour tax has caused the consumers price to rise and the firms price to fall. In the new equilibrium the difference between the two prices is equal to the tax: $5/hour. The higher price for consumers and lower price for firms results in lower equilibrium quantity. The diagram treats the tax as a shift in supply, which is how things look to consumers. It would also be possible to have a shift in demand, which is how things looks to sellers. d) Based on your graph from part (c), do you think that the degree of price pass through for consumers is greater than 50 percent? That is, does the tax of $5 per hour result in more than a $2.50 per hour increase in the consumers price? (3 pts) It is evident from the graph that the price to consumers increases by less than $2.50/hour and the price received by firms falls by more than $2.50/hour. Thus, there is less than 50 percent pass through for consumers....
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