PP210A Problem Set #2

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Problem Set #2

PP210A

Question #1 (Problem 4.2 from Nicholson 9th edition)

(A). A young connoisseur has $300 to spend to build a small wine cellar.  She enjoys two vintages in particular: a 1997 French Bordeaux (wf) at $20 per bottle and a less expensive 2002  California varietal wine (wc) priced at $4.  How much of each wine should she purchase if her utility function is

(B). When she arrived at the wine store, she discovered that the price of the French wine had fallen to $10 a bottle because of a decline in the value of the euro.  If the price of the California wine remains stable at $4 per bottle, how much of each wine should she purchase to maximize utility under these alternative conditions?

Question #2

When the price of gasoline is $1 per gallon you consumer 1000 gallons per year.  Then two things happen: (1) the price of gasoline rise to $2 per gallon, and (2) a distant uncle dies with the instructions to his executor to send you a check for $1,000 a year.  If no other changes in prices and income occur, do these two changes leave you better off than before?  Use a graph to illustrate your answer (you can graph consumption of all other goods on the vertical axis and gasoline consumption on the horizontal axis).

Question #3

Suppose that an individual spends all of her money on gasoline (G) and a composite good (C) representing all other consumer goods.  The person’s utility function is given by the equation U = GC, the price of gasoline is equal to one dollar (PG=1), and the price of the composite good is equal to one dollar (Pc=1).  The person’s income is equal to $100.

(A) Given the utility function and current prices, what are the optimal levels of C and G?  Calculate the utility received from this consumption bundle by plugging the optimal levels back into the utility function.

(B) Now suppose that the price of gasoline increases to $4 per gallon.  Calculate the new optimal levels of consumption for gasoline and the composite good.   Again, plug the new levels into the utility function.  Has the price increase impacted this person’s level of happiness?

(C) Looking at the change in the consumption level of the composite good, which effect of the increase in the price of gasoline dominates, the income effect, the substitution effect, or neither?

(D) The increase in the price of gasoline will cause both income and substitution effects that reduce the level of gasoline consumption.  On the other hand, the income and substitution effects on consumption of the composite good caused by the increase in the price of gasoline will push in opposite directions.  Decompose the total reduction in gasoline consumption and the change in the composite good consumption into the income and substitution effects caused by the price increase.

NOT SO SUBTLE HINT: The substitution effect is defined as the reduction in gasoline consumption (or the increase in the composite good consumption) that would occur in response to the change in prices if we were to hold utility constant at the pre-change level.  Two conditions from the maximization problem provide the information necessary to solve for the substitution effect: (1) the condition that utility equal the pre-increase level – i.e., U = GC = pre-expansion level calculated in part (A), and (2) the requirement that MRSGC (calculated using UG/UC equal the new ratio of prices after the price increase.  These equations provide the two equations needed to solve for two unknowns.  Once you have calculated the substitution effects on G and C, the income effects are the remainders of the total effects not explained by the substitution effects.

(E) Draw a graph showing the initial budget constraint, the post-increase budget constraint, the pre-increase consumption bundle, the post-increase consumption bundle, and the income and substitution effects of the price increase on the consumption of gasoline and the composite good – i.e., the whole enchilada.

(F) You have been hired by the Bureau of Labor Statistics to analyze the inflationary impact of the price increase.  They want you to calculate two statistics: (1) the amount of additional money needed (above and beyond the individual’s income) to restore this individual’s utility level to her pre-increase utility level, and (2) the amount of additional income this individual would need to be able to consume the pre-increase consumption bundle.  What are these numbers?  Which is greater?  Which would be a more accurate measure of the loss in purchasing power caused by the price increase?

Question #4

Suppose that the demand for crossing the Golden Gate Bridge is given by 10,000 - 1000P.

(A) If the toll (P) is $2, how much revenue is collected? (Revenue given by quantity times price).

(B) What is the price elasticity of demand at this point?

(C) Could the bridge authorities increase their revenue by changing their prices?

(D) A company begins to compete with the Golden Gate bridge by operating hovercrafts that makes commuting by ferry much more convenient.  How would this affect the elasticity of demand for trips across the Golden Gate Bridge?

Question #5: When your economics professor was 10 years old (1978), a pack of baseball cards cost $0.25.  Assuming that the only factors influencing the price of a pack of new baseball cards is inflation, how much would a pack cost in today’s dollars.  You’ll need to visit the Bureau of Labor Statistics webpage to find data for the Consumer Price Index.  Use the all-urban consumers series.

Question #6: Explain with graphs why an inflation index based on a fixed consumption bundle overstates the rate of inflation when one’s preferences are described by downward sloping indifference curves with a diminishing marginal rate of substitution.

Suppose that someone’s preferences are described by L-shaped indifference curves (the case of perfect complements).  Is this person willing to substitute one good for another when prices change?  If preferences are described in this manner, does the inflation index described above still overstate the inflation rate?  Can you think of an example where such preference may be relevant?

Question #7:  Incidence of a Wage Subsidy

In this question, we are going to analyze how a public wage subsidy to low-wage workers may in part subsidize the labor costs of employers in the private sector and what factors determine how much of the subsidy is captured by low-wage workers.  The analysis here is very similar to the analysis one might conduct of the “incidence” of a tax, where incidence refers to the proportion of a tax that would be paid by the consumers and the proportion implicitly paid by producers.

Let W be the market clearing wage for low-skilled workers.  The demand for low-skilled workers is defined by the equation

where ED is employment demand, both α and β are positive numbers, and β can be thought of as a gauge of the sensitivity of labor demand to changes in wages.  Labor supply is given by the equation

where ES is labor supply, γ and δ are both positive numbers and δ can be thought of as a gauge of the sensitivity of labor supply to changes in wages.

The market clearing wage is defined by the condition

(a) What is the minimum wage below which nobody will work?

(b) Solve for the market clearing wage in terms of the parameters α, β, γ, and δ.

(c) Suppose that we institute a wage subsidy for low-wage workers such that the wage faced by these workers is equal to W+s.  Note the wage faced by employers is still equal to W.  Using the equation solve for the new equilibrium wage in terms of the parameters α, β, γ, δ, and s.

(d) Label your answer to part (b) W0 and your answer to part (c) W1.  Hence, the after subsidy wage is given by W1 + s when we institute the subsidy while the net wage in the absence of the subsidy if W0.

· Calculate the difference between W1 + s and W0 in terms of the parameters β, δ and s.

· Do workers receive the full subsidy value s?

· How does the portion of the subsidy that workers received depend on β, δ?  Can you offer an intuitive interpretation of your answers to this question?

(e) Use a supply-demand graph to illustrate the analysis that you just performed. You don’t need to use the actual parameters of the problem, but model labor supply, labor demand, the market clearing wage and employment level, and how a subsidy will shift the employment equilibrium to the right.  Note, you simply have to highlight the point where the wedge between wage paid and wage received equals the size of the subsidy to see how incidence of the subsidy will be distributed across workers and firms.


2023-09-25