1. a) Since both commodities have to be consumed in fixed proportions, there will be no substitutability within the goods. So the IC’s will be L-shaped.
b) In the first case no indifference curve will exist. Since Monica can dispose of pistachios freely, consuming none to consuming any positive amount of pistachios will be preferred. Further for any given level of pistachio, more ice-cream will be preferred. The vertical axis will be the preferred set since it contains zero pistachio. However since every movement upward will provide greater satisfaction to the consumer has she gets more ice-cream for the same level of pistachio, higher points will be preferred to lower one along the vertical axis. Thus, not indifference relation exists within any points in the ice-cream- pistachio space under the assumption of free disposal.
In the second case, the IC map will be as shown in the following diagram:
Here, the positive slope of the IC is due to the fact that as Monica hates Pistachio, only consuming more of ice-cream can make her tolerate pistachio. The IC is backward bending since as her consumption of both rises gradually more and more units of ice cream are required to compensate the loss in utility resulting from an additional unit of Pistachio consumption.
1.c) This is simply the case where the consumer has preference for both goods and thus we get an IC with normal properties.
1.d) In this case, due to the love of dogs irrespective of breed, yellow labs and beagles are perfect substitutes for the consumer and thus the IC will be a downward sloping straight line.
1. e) No IC will exist in this case since the first judgement will always be preferred to the second. The case is analogous to the case of free disposal.
b) The tangency condition implies that at equilibrium the marginal rate of substitution shall be equal to the relative price ratio. Since the relative price ratios faced by both Eric and Bill shall be equal, the marginal rates of substitution shall also be equal at the respective equilibrium points. However, for all other points they will be different.
Though both IC’s shall be negatively sloped, Bill’s IC which runs through his preferred bundle shall be relatively flatter than Eric’s IC which runs through his preferred bundle.
Here, the horizontal stretch on the food axis is due to the increase of $1000 in income which can be utilised only in consuming food.
Here, due to the existence of the black market, an additional $1000 income of food stamps can be converted into 500 units of AOG given the black market price.
4. a) Since the income of each consumer is $120, the maximum amount of other goods purchasable is 120 units and the maximum amount of swimming hours purchasable is 60. Thus the budget line will be the locus of the coordinates (0,120) and (60, 0).
Jen chooses to swim 20 hours a week implying a cost of $40. So she disposes $80 in the purchase of all other goods. Thus Jen’s bundle will have the coordinates (20, 80).
Similarly the commodity bundles of Tom and Roger can be calculated to be (40, 40) and (20, 50) respectively.
b) i)In this case, the total income for each can yield a maximum of 80 swimming hours since of $120 weekly income, $40 will have to be paid for membership, and at the reduced price the remaining $80 can purchase $80 swimming hours. So the new budget line will be as shown in the diagram below.
ii) All the swimmers are better off under the new policy. This is shown clearly in the following diagram.
Observe, if each swimmer retains his/her earlier consumption of either all other goods or swimming, under the new policy he/she can consume more of the other. Thus, it can unambiguously stated that each swimmer shall be better off due to the new policy.