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Intermediate Microeconomics - Wissink BRIEF ANSWERS TO PROBLEM SET #
- The demand systems would be as follows: For u=ax+by you get either one corner or the other depending on how a/b compares to the price ratio. So, x=I/px and y=0 when a/b>px/py and y=I/py and x= otherwise (Note that when a/b = px/py I have opted to consume only y. Really, any combination of x and y would work in that knife edge case.)
For u=min{ax, by} you have to recognize that you always want ax=by. Therefore x=(by)/a. Now plug that into the budget line and solve for y and you get: pxx+pyy=I where x=(by)/a. You eventually get: y=(aI)/(bpx+apy) and x=(bI)/(bpx+apy).
- The Price Consumption Curve (PCC) (or price offer curve)for a change in the price of x looks as follows:
y
x
PCC
u=xy
p /px y = 1
PCC
y
x u=x+y
y
x
PCC
u=min{x,y}
y
x
u=xy
E
E
E
H
- The Income Consumption Curves (ICC) - or income offer curves - look as follows:
ICC
u=xy
y
x
ICC
u=min{x,y}
y
x
- The income and substitution effects for an increase in the price of x look as follows: Note: the total effect will be E 0 to E 1 , the substitution effect from E 0 to EH and the income effect from EH to E 1.
water
$aog E 1
E 0
IC
IC
1
0
- If the wage rate increases that makes leisure relatively more expensive and at the same time increases your income or purchasing power. (Note this is different than in the case of a price increase for a typical commodity.) The substitution effect would say consume less leisure (supply more labor) since leisure is now more expensive, but the income effect - assuming leisure is a normal good - would say demand more leisure (supply less labor) now that you have higher real income. If the income effect outweighs the substitution effect, an increase in the wage rate will bring about a reduction in labor supply; you will generate a backward bending supply curve for labor. 9. a. See graph Note: The quantity of water demanded must decrease. The entire policy, i.e., the tax and rebate, will isolate the pure substitution effect and under the usual assumptions this implies that water consumption necessarily declines.
b. Would the tax alone do it? Depends: if H 2 0 is a normal good in this range of economic activity, then yes. If H 2 0 is inferior, then it depends on the sizes of the IE and SE.
c. Consumers are better off: IC 1 is better than IC 0
d. Yes, just give them enough of a rebate to be back in IC 0.
- a. False, unless it happened to be the case that px = py. A rational utility maximizing consumer equates the marginal utilities per dollar across all goods consumed, i.e., MUx/Px = MUy/Py.
b. False: The consumer can spend all his income and not equate the MRS to the ERS and still be maximizing utility if he happens to be in a corner solution situation like with perfect substitutes and/or perfect complements.
c. Not necessarily. How about if the consumer equates the MRS to the ERS but does not spend all his income? Also, for example, take the case of preferences that gave us "bowed-out" indifference curves. Utility is not maximized at the bundle on the budget line where the ERS = MRS.
