The demand function is Q = 100 -.5P. The cost function is TC = C = 100 + 60(Q) +(Q)2
a. Find MR and MC. b. Demonstrate that profit is maximized at the quantity where MR = MC. c. Derive the relationship between marginal reve-nue and the price elasticity of demand, and show that the profit-maximizing price and quantity will never be the unit-elastic point on the de- mand curve.
d. Using the information in (b), demonstrate that the profit-maximizing price and quantity will never be in the inelastic portion of the demand curve
7 Explain the competitive process when a firm earns a positive economic profit.
8 Explain what is different between firms in mo- nopolistic competition and firms in oligopoly. What does this difference mean for prices and quantities and for economic profit?
9 A firm has estimated the following demand function for its product:
Q = 8 - 2P + 0.10I + A
where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands. Assume that P=$10,I=100,andA=20. Based on this information, calculate values for: quantity demanded; price elasticity of demand; income elasticity of demand; and advertising elasticity. (Use the point formulas to complete the required elasticity calculations)
10 The market supply and demand functions for a product traded on a perfectly competitive market are given below:
QD = 40 - P QS = -5 + 4P
Based on this information, calculate the equilibrium price and quantity in this market.
11 Now, suppose the competitive market in Exercise10 is monopolized. Calculate the price and quantity for the monopolist.