The demand function is Q = 100 –.5P. The cost function is TC = C = 100 + 60(Q) +(Q)2a. 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 curve7 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 + Awhere 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 + 4PBased 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.
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