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MoreExercisesOnMonopoly - Monopoly A single-price...

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Monopoly A single-price monopolist has constant Marginal Cost. The current price and quantity are P*=10 and Q*=20, an equilibrium in which the price elasticity of demand ε is -2. 1. What is the value of the Marginal cost? 2. What is the equation of the linear demand curve? 3. What is the Marginal Revenue curve of the monopolist? 4. What is the Consumer surplus? 5. What is the Monopolist surplus? Answer: 1. From the Inverse Elasticity Pricing Rule (IEPR) we have (P*-MC)/P*=-1/ε. Equivalently, MC=P*(1+1/ε). Hence MC= 10*(1-1/2)=10*(1/2)=5. 2. Since the elasticity at P=10 and Q=20 is -2, then -2=-b*(10/20) where b is the parameter in the aggregate linear demand Q=a-bP. Hence b=4. Since the demand goes through the point P=10, Q=20, then we can see that a=60. Hence the market demand is Q=60-4P. 3. The inverse demand is P=60/4-Q/4=15-0.25Q. Hence the Marginal Revenue curve is MR= 15-0.5Q. 4. CS=[(15)-10]*(20)/2=50. 5. Monopolist’s Surplus: (10-5)*20= 100. A single-price monopolist produces silver whatnots and faces a linear demand Q=100-2P (Q is measured in thousands of whatnots and P is measured in thousands of dollars per thousands of whatnots). The Monopolist Marginal Cost is MC(Q)=3Q. 1. What is the equation of the Marginal Revenue curve? 2. Find the equilibrium. 3. Compare with a competitive market in which the demand is Q=100-2P and the market inverse supply is P=3Q. Assume now that the government imposes an Excise tax of T=2 thousands dollars on each unit of Q (hence $2 per whatnots).
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