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CSUN ECON 500 - Examination 2

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ECON 500 A. Key Examination 2 - Spring 2005 1. While shopping in the produce section of Albertsons you overhear someone say: “I don’t like broccoli. In fact, I would have to be paid a positive amount of money to be willing to increase my consumption of broccoli!” Let =1x (pounds of broccoli) and =2x (dollars spent on everything else). a) Based upon this statement, what can you infer about 1MU (the marginal utility of broccoli) for this individual? Explain. (6 points) Recalling that 1MU provides a measure of the change in utility as the level of consumption of 1x is increased (with 2x fixed), the statement suggests that 01<MU . b) Recalling that the slope of an indifference curve is given by 212,1MUMUMRS −=− , what can you infer about the indifference curves of this individual? Explain. (6 points) Since 01<MU , it follows that 0212,1>−=−MUMUMRS . This implies that the indifference curves are positively sloped. c) Based upon the insights made thus far graphically illustrate the solution to this individual’s utility maximization problem, and identify the optimal level of consumption of both 1x and 2x . (6 points) In order to maximize utility, will optimally consume 0*1=x units of broccoli and 2*2pIx= units of “other goods,” as illustrated below: 2x 1x0*1=x 0 2*2pIx=Strict Upper Contour Set to *XBudget Set2. Consider the market for “Good X.” Demand is given by ppD 500000,10)( −= and supply is given by ppS 750)(=. a) State the “Law of Demand,” and explain whether or not the “Law of Demand” is satisfied in this market. (6 points) The “Law of Demand” state that holding all other factors fixed, there is an inverse relation between price and quantity demanded. For the function ppD 500000,10)(−= this Law holds, since for every one unit increase in price, quantity demanded will decrease by 500 units. b) Is there “excess demand,” “excess supply,” or neither at a price of 8=p ? Explain. (6 points) Since 000,6000,4000,10)8(=−=D and 000,6)8(=S (so )8()8( SD = ), we observe that there is neither excess demand nor excess supply at a price of 8=p. c) Graphically illustrate supply and demand, and identify *p and *q (the equilibrium price and equilibrium quantity). (8 points) d) Suppose there is a decrease in the price of a good which consumers view as a substitute for “Good X.” Clearly explain how this change would affect the market for “Good X” (i.e., explain how, if at all, demand, supply, equilibrium price and equilibrium quantity in the market for “Good X” would each change). (8 points) If the price of a good which consumers view as a substitute for “Good X” were to decrease, this would lead to a decrease in demand for “Good X” (with no change in supply). As a result, equilibrium price and quantity must both decrease. Supply Demand p q 000,6*=q 8*=p3. Consider the market for gasoline in Northridge. Between January 2005 and April 2005, equilibrium price increased from $2.279 to $2.549, while equilibrium quantity decreased by 5,000 units. Clearly explain whether or not this observed change could be a result of: a) a decrease in Supply with no change in Demand. (10 points) The observed increase in price and decrease in quantity could be a result of a decrease in supply with no change in demand, as illustrated below: b) a simultaneous increase in both Supply and Demand. (10 points) A simultaneous increase in both supply and demand would have to lead to an increase in equilibrium quantity, as illustrated below (the magnitude of this increase depends upon where the New Demand curve intersect the New Supply curve drawn in the figure below). Thus, the observed increase in price and decrease in quantity could not be a result of such a change in supply and demand. Demand Initial Supply New Supply p q Demand New Supply Initial Supply p q4. Consider a consumer with 221)( xxXU = . For this individual, 221xMU = and 2122 xxMU = . a) Does this individual have “Monotonic Preferences”? Explain. (6 points) Yes, this consumer has “monotonic preferences.” Since both 221xMU = and 2122 xxMU = are each never negative, we know that regardless of the current consumption bundle, this consumer finds that for each good “more is better.” b) Specify 2,1MRS as a function of 1x and 2x . (6 points) 122122212,122 xxxxxMUMUMRS=== . c) State two equations (i.e., two conditions) which the utility maximizing levels of 1x and 2x must satisfy. (8 points) A consumer with Cobb-Douglas preferences maximizes his utility by: i. “spending all income” ⇒ Ixpxp=+2211 ii. “consuming where his marginal rate of substitution is equal to the price ratio” ⇒ 212,1ppMRS = ⇒ 21122 ppxx= d) Determine the utility maximizing consumption bundle for this consumer (that is, solving the equations stated in part (c), determine the optimal levels of 1x and 2x , each as a function of prices and income). (8 points) Rearranging condition (ii) above, we see that the optimal consumption bundle must satisfy 11222 xpxp=. Together with condition (i) this implies Ixp =113 or 1*13pIx = . Substituting this expression into condition (ii) and solving for 2x gives us 2*232pIx = .e) How will the utility maximizing consumption bundle of this consumer change if income and both prices simultaneously increase by 5% (so that initialnewII )05.1(= , initialnewpp,1,1)05.1(=, and initialnewpp,2,2)05.1(= )? Clearly explain. (6 points) This simultaneous change in prices and income will not alter the utility maximizing consumption bundle of this consumer. One way to observe this is to recognize that such a change in prices and income will have no impact on the “set of feasible bundle” from which this individual must choose (the initial budget constraint is initialinitialinitialIxpxp =+2,21,1; the new budget constraint is newnewnewIxpxp=+2,21,1 or equivalently initialinitialinitialIxpxp )05.1()05.1()05.1(2,21,1=+ , which can be written as initialinitialinitialIxpxp=+2,21,1). Alternatively, we can examine the demand functions derived in part (d) above, and see that the new levels of consumption are *,1,1,1*,13)05.1(3)05.1(initialinitialinitialinitialinitialnewxpIpIx=== and *,2,2,2*,232)05.1(3)05.1(2initialinitialinitialinitialinitialnewxpIpIx=== .EXTRA CREDIT - 3 points! Michael has dial-up Internet access provided


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CSUN ECON 500 - Examination 2

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