Lizzie’s Lingerie started selling robes for $36, adding a 50 per cent mark up on cost. Costs were estimated at $24 each: the $10 purchase price of each robe, plus $6 in allocated variable overhead costs, plus an allocated fixed overhead charge of $8. Customer response was such that when Lizzie’s raised prices from $36 to $39 per robe, sales fell from 54 to 46 robes perweek.
a. Estimate the optimal (profit maximizing) pricing strategy assuming a linear demand curve.
b. Estimate the optimal pricing strategy assuming a power demand curve.
c. Explain why there is a difference between the above two strategies.
d. Estimate the size of the profit at both prices, assuming a power demand curve.
e. Estimate the optimal price if the cost of buying the robes rises from $10 to $11, assuming a power demand curve.
2. Crystal Ball Corp. has estimated its demand and cost functions as follows:
Q = 80 5P
C = 30 + 2.2Q + 0.5Q 2
Where P is in $, Q is in thousands of units and C is in $,000.
a. Calculate the profit maximizing price and output.
b. Calculate the size of the above profit.
c. Calculate the price elasticity of demand at the above output; is demand elastic or inelastic here? What should it be?
d. Calculate the marginal cost at the above output.
e. If unit costs rise by $2 at all levels of output and the firm raises its price by the same amount, what profit is made?
f. What is the profit maximizing strategy given the above rise in costs?
g. How much profit is the firm forgoing by raising its price $2?