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Answers_Practice2 - University of Wisconsin Economics 301...

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- ---- - - - - - - - - - University of Wisconsin Economics 301: Intermediate Microeconomic Theory Korinna K. Hansen Answers to Practice Problems (part 2) 1). a). False. The utility function gives us information about risk aversion and not the price of t1I'1 insurance. Risk averse individuals exhibit diminishing marginal utility. TU Tu 1L{ b). True. To derive the aggregate demand for a p private good, we need to add up the two demand curves horizontally. We add up the quantities at each price. x = Xl + X2 = 1,000 -2p +500 - p. Therefore X= 1,500 - 3p for p<500. 500 I ~ p= 500 =- .3 r ISOO X - c). True. With the reduction in the barley crop, the supply will decrease and cause the price of barley to increase. At the higher price less will be exchanged. Since the demand is elastic the decrease in quantity will be larger than the increase in price, and total revenues will therefore fall. (Remember dR/dq = p (1- lie)). d). True. We can use the equation for the elasticity of demand here e= (dq/dp )(p/q) = (1/slope) (p/q) and calculate the elasticity at the two prices 10 and 20 cents. The slope of this linear demand curve is - 1/10. When the price is 10 cents, x = 999 and when the price is 20 cents, x = 998. Then the elasticity at p = 10 cents: e = (-10) (0.1/999) = -0.001 and the elasticity at p=20 cents: e = (-10) (0.2/998) = -0.002. So as the price of potatoes changes from 10 to 20 cents the price elasticity of demand increases in absolute value. e). True. The elasticity of demand is e= (dq/d~)(p/q), and q = 2/p. Therefore, dq/dp = 2(_1)p-2 and p/q = p/(2/p) = p2 12 . Then e= 2(_l)p-2) (p 12) =-1 f). True. To add up the two demand curves horizontally we first need to solve them for the quantities and we have Xl = 15 - P and X2 = 20/3 -1/3 p. Then the aggregate demand will be X=Xl+X2 = 15 - P + 20/3 -1/3 P = 65/3 - 413 p. So, X= (65/3) - (413) P and if we put p=ll in the aggregate demand equation we find that x = 65/3 -(4/3) (11) =21/3 =7 g). True. The consumers will pay more than half the P tax if their demand is relatively more inelastic than l' P,'t the producer supply. Similarly, the producers will ~~rt'v pay more than half the tax if their supply is relatively more inelastic than the consumers demand. The party Pl. with the most inelastic curve pays most of the tax. P.3 tt P !'OJ ~ C e.-r fh'l'(.f .... ~o? -£-Q.)(

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5 f h). False. If the amount of the good supplied is independent R -=(1 of the price, then the supply curve is perfectly inelastic. B. I Initial equilibrium quantity and price are at ql and Pl. Then after tax consumers will still pay PI = P2, but producers receive the lower price P3, and not PI anymore. The difference PI-P3 = quantity tax. &1, ~ i) False. If you double both inputs f(2XI, 2X2)= min (4XI+2X2, 2XI+4x2) = 2 min (2XI+X2, xI+2x2). So, this technology exhibits constant returns to scale. j). True. The technical rate of substitution, TRS = MPIIMP2 l12 l12 MPI = 2 (2 XI+ 4X2r (112) and MP2 = 4 (2 XI+ 4X2r (112). Therefore TRS = 1;2 k). False. This firm could experience constant, increasing or decreasing returns to scale depending on the specific functional form of the production function f(XI, X2) = axl+bx2.
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