Question

1. Suppose the demand function for beer is given by q = 2000−40pb + 20pw + 0.1Y , where pb is the price of beer, pw is the price of wine, and Y is income. If pb = $10, pw = $20, and Y = $5,000, how much would the price of beer need to rise for the quantity demanded to fall to 1300 units?
2. Suppose the supply curve for labor is given by qs = w + 10, and the demand curve is given by qd = 130−3w, where w is the wage rate. What is the equilibrium wage rate and output?
3. Suppose the supply curve for labor is given by qs = w+10, and the demand curve is given by qd = 130−3w, where w is the wage rate. How many workers will become unemployed if the government mandates a binding minimum wage of $40?
4. Suppose Hansel and Gretel are the only two consumers in the market for apple cider. Hansel’s (inverse) demand curve for apple cider is p = 5−0.5Qd, and Gretel’s (inverse) demand curve is p = 5−Qd. Write the market demand curve.

Answer 1

Question 1

Current price of beer, Pb = $10

Calculate the price when quantity demanded is 1,300 units -

q = 2000 - 40Pb + 20Pw + 0.1Y

1300 = 2000 - 40Pb + (20*20) + (0.1*5000)

1300 = 2000 - 40Pb + 400 + 500

1300 = 2900 - 40Pb

40Pb = 1600

Pb = 1600/40 = 40

The price of beer is $40 when quantity demanded is 1,300 units.

So,

The price of beer need to rise by ($40 - $10) $30 for the quantity demanded to fall to 1,300 units.

Question 2

Supply curve is as follows -

Qs = W + 10

Demand curve is as follows -

Qd = 130 - 3W

In equilibrium, demand equals supply

Qd = Qs

130 - 3W = W + 10

4W = 120

W = 30

Q = 130 - 3W = 130 - (3*30) = 130 - 90 = 40

Thus,

The equilibrium wage rate is $30.

The equilibrium output is 40 units.