Value: 60 points--30% of grade. All work must be shown or explained to earn credit.

1. Amalgamated Popcorn sells bags of flavored gourmet popcorn at a local mall. The daily demand for bags of popcorn is:

Q = 500 - 100P + 1.25A - 20P_S + .002I

where P_S is the price you Amalgamated charges for a soda pop (currently $1), A is advertising (currently $200), and I is per capita income ($12,000).

a. If the price of a bag of popcorn is $1, how many bags will Amalgamated sell a day and what are its daily revenues from popcorn? (4)

b. Determine the price elasticity of demand for popcorn at a price of $1. (4)

c. Based on your answer, what advice do you have for Amalgamated? (2)

d. Determine the income elasticity of demand for popcorn. What does your result say about the good? (4)

e. If Amalgamated raises price to $1.50 a bag, determine the arc price elasticity of demand. (4)

2. Nearby College has estimated the following elasticities: price elasticity (-1.6), income elasticity (0.8), cross-price elasticity with respect to Competition College's tuition (0.25).

a. If tuition at Competition is set to rise at 8%, how will Nearby's enrollments change? (2)

b. If income's are expected to rise from $20,000 to $22,000, what is the effect on Nearby's enrollments? (3)

c. If the marginal cost of a student is constant at $2750, what tuition should Nearby charge to maximize profit? (4)

3. Your company sells aluminum products to two different markets, A and B, with demands:

Q_A = 10,000 - 40P_A and Q_B = 8000 - 60P_B.

Total cost TC=75Q so that marginal cost is 75.

a. What are the optimal prices and quantities in each market if you can price discriminate? (6)

b. Suppose that you can be a 1^st degree (perfect) price discriminator in market A, determine the maximum possible profits from market A. Hint! A diagram may be useful. (4)

4. Dirt Diggers (DD) excavates roadside ditches for laying drain pipe. Its production function is:

Q = 10L - 0.1L² where Q is the length of the ditch in meters and L is labor hours.

a. Explain whether the production function is consistent with the law of diminishing returns. (3)

b. How many hours of labor should the firm hire if it can hire labor at $12 per hour and it can charge customers $2 per meter? (5)

5. Falls Ambulance Service has the following production function: for ambulance deliveries per day:

Q = L^0.4K^0.6.

1. Show or verify that the production function has constant returns to scale. (2)

b. Determine the MRTS_LK. (4)

c. Derive the equation for the isocost line representing a cost of $1000 where the price of labor is $8 per unit and the price of capital is $6 per unit. (3)

d. If the price of labor is $8 per unit and capital is $6 per unit, and Falls has a daily budget of $1000, determine the maximum ambulance deliveries it can make. (6)

ANSWERS:

1a. Q=654, TR=654; b. Ep=-0.15; c. raise P (to get out of inelastic range of demand); d. Ey=0.04 (normal good) e. Arc Ep=-0.20
2a. 2% increase; b. 8% increase; c. P=7333
3a. QA=3500 and PA=162.5; QB=1750 and PB=104; b. $612,500 (area under demand curve and above 75)
4a. MPL=10-0.2L; b. L=20
5a. Double inputs, output doubles; b. MRTS=(2/3)(K/L); c. 1000=8L+6K; d. Q=76 (from equilib condition you will find that K=2L, then substitute into TC equation to find L=50 and K=100)