1 In the application aggregating the demand for broadband se

1. In the application \"aggregating the demand for broadband service\" (based on duffy-deno, 2003), the demand function is Qs=5.97p^0.563 for small firms and Q1=8.77p^0.296 for larger firms, where price is in cents per kilobyte per second and quantity is in millions of kilobytes per second (kbps). What is the total demand function for all firms? If the price for broadband service is 40 cents per kbps, what is the equilibrium quantity demanded by small, large firms, and all firms?

2. If the US Supply function of corn is Qa=10+10p and the supply function of the rest of the world is Qr=5+20p, what is the world supply function? (Hint: Note that there is a kink in the world supply function.)

3. Using calculus, determine the effect of an increase in the price of beef, Pb, from $4 to $4.60 on the equilibrium price and quantity in the Canadian pork example. (Hint: Conduct an analysis that differs from that solved in Question 2 in that the shock is to the demand curve rather than to the supply curve.) Illustrate your comparative statics analysis in a figure.

4. Suppose the demand function for carpenters is Q=100-w, and the supply curve is Q=10+2w-T, where Q is the number of carpenters, w is the wage, and T is the test scored required to pass the licensing exam. By how much do the equilibrium quantity and wage vary as T increases?

5. What effect does a $1 specific tax have on equilibrium price and quantity, and what is the incidence on consumers, if the following is true:

a. The demand curve perfectly inelastic.

b. The demand curve is perfectly elastic.

c. The supply curve is perfectly inelastic.

d. The supply curve is perfectly elastic.

e. The demand curve is perfectly elastic and the supply curve is perfectly inelastic.

Use graphs and math to explain your answers.

Solution

(1)

Total demand, Q = Qs + Q1 = 5.97 x p^0.563 + 8.77 x p^0.296

When p = 40,

Qs = 5.97 x p^0.563 = 5.97 x (40)^0.563 = 5.97 x 7.98 = 47.63

Q1 = 8.77 x p^0.296 = 8.77 x (40)^0.296 = 8.77 x 2.98 = 26.13

(2)

World supply function = Qa + Qr = 10 + 10p + 5 + 20p = 15 + 30p

(3)

Canadian pork example is not provided!

(4)

In equilibrium, demand = supply

100 - w = 10 + 2w - T

3w = 90 + T

w = (90 + T) / 3 = 30 + 0.33T

So, as T increases, equilibrium wage increases (since T has a positive coefficient). Higher value of wage will reduce the demand of carpenters.

NOTE: First 3 (answerable) questions have been answered.