Q17) 1) (250 points; 12 minutes) Decide whether each of the following statements is True, False, or Uncertain, and give a brief but clear explanation of your answer. (Most of the credit will be given for the explanation.)

1a) When an aluminum company made 100,000 cans, the last unit cost $0.02. The next year it made 500,000 cans and the last unit cost $0.04. This company does not benefit from economies of scale.

1b) A demand equation for gasoline is estimated to be: Ln Q = -0.54 - 0.40 Ln P + 0.25 Ln Income where Q is in millions of gallons per week and the price is per gallon. A refinery fire leads to a price increase from $1.00 per gallon to $1.50 per gallon. Since the above equation implies that gasoline demand is inelastic, the quantity demanded will drop by less than 1%.

2.      (350 points; 18 minutes) A railroad which runs between two cities 'produces' two products: passenger and freight service. The marginal cost of carrying an extra ton of freight is $0, and the marginal cost of carrying an extra passenger is $0.

There are joint, fixed costs of $19,000 per day. There is no other competitor in this market. The daily demand for passenger service is

Pp = 8 - 0.005Qp with Qp the number of passengers and Pp the price of a two-way ticket.

The daily demand for freight service is Pf = 10 - 0.001Qf with Qf in tons and Pf the price per ton. Currently, Pp=$5 and Pf=$8, so that Qp= 600 and Qf=2000. The revenues from passenger service are $3000 and from freight $16,000.

The firm currently assigns overhead to products on the basis of their dollar share of revenues.

Thus, the costs allocated to the passenger business are $3,000, while those allocated to freight are $16,000. T

he firm's accountants argue that prices should be raised on both products, since the firm barely breaks even.

What pricing would you recommend? Evaluate the accountants' argument. Would your conclusions differ if the fixed costs were $30,000 per day?

Answer 1

1(a) When an aluminum company made 100,000 cans, the last unit cost $0.02. The next year it made 500,000 cans and the last unit cost $0.04. This company does not benefit from economies of scale.

→ The above statement is either False or Uncertain.

Explanation:- The last unit cost represents the Marginal Cost which the firm incurs in order to increase its output by 1. Economies of scale is a concept based upon falling average cost. Here, we see the Marginal cost increase from $0.02 to $0.04 when the company increases its output from 100,00 cans to 500,000 cans. We cannot determine average costs from this. So economies of scale may or may not be present.

(b)A demand equation for gasoline is estimated to be: Ln Q = -0.54 - 0.40 Ln P + 0.25 Ln Income where Q is in millions of gallons per week and the price is per gallon. A refinery fire leads to a price increase from $1.00 per gallon to $1.50 per gallon. Since the above equation implies that gasoline demand is inelastic, the quantity demanded will drop by less than 1%.

→ The above statement is False.

Explanation:- From the expression - 0.40 Ln P we can understand that the firm's own-price elasticity of demand is E_p = -0.40.

Now, Own price elasticity of demand E_p = ?PercentChangeInPricesPercentChangeInQuantity??

Price increases from $1 to $1.50. This means the price increases by ?1.01.5−1.0??*100 = 50%.

This means, demand should change by:

%Change In demand = E_p x %Change In price

%Change In demand = -0.40*50% = -20%

So demand should drop by 20% and not less than 1% as given in the statement.

Answer 2

Calculations for the passenger market

Fixed costs FC = $19,000; MC = $0; Inverse Demand function P_p = 8 - 0.005Q_p

From this, we get the Total Revenue TR = Price X Quantity = 8Q_p - 0.005Q_p²

Hence, Marginal Revenue MR = ?dQd??TR = 8 - 0.01Q_p

At optimum quantity, MR = MC

→ 8 - 0.01Q_p = 0

→ Q* = 800 units.

This gives us the optimum price P* = 8 - 0.005Q* = 8 - 4 = $4

Total revenue TR = 800*$4 = $3,200

Calculations for the freight market

MC = $0; Inverse Demand function P_f = 10 - 0.001Q_f 

From this, we get the Total Revenue TR = Price X Quantity = 10Q_f - 0.001Q_f²

Hence, Marginal Revenue MR = ?dQd??TR = 10 - 0.002Q_f

At optimum quantity, MR = MC

→ 10 - 0.002Q_f = 0

→ Q* = 5000 units.

This gives us the optimum price P* = 10 - 0.001*5000  = 10- 5 = $5

Total revenue TR = 5000*$5 = $25,000

Combined Calculations

Total revenue from both services = $25,000 + $3,200 = $28,200

Since the firm has no MC, the total profit = $28,200 - $19,000 = $9,200

What pricing would you recommend? Evaluate the accountants' argument. Would your conclusions differ if the fixed costs were $30,000 per day?

→ As per the calculations done above, the optimal price for passenger service should be $4 while that of freight service should be $5.

The accountants argument seems invalid. The firm is making a profit ($9,200) so the current fixed costs need not be considered for evaluating optimum pricing.

Incase the fixed costs were $30,000 per day, the daily profit would turn negative. At this point, the firm should shut down.