Question

Suppose that a city operates two neighborhood schools, one in
the rich neighborhood and one in the poor neighborhood. The schools
are equal in size and currently have equal budgets. The city
receives $10 million in federal grant money that can be used to
supplement the budgets of the two schools, which are initially
identical. For each school, the average score on a standardized
achievement test depends on how many dollars are allocated to the
school. Letting *S* denote the average test score and
*X* denote additional spending in millions of dollars, the
relationships between scores and additional spending for the two
schools are as follows:

*S*_{poor} = 40 +
*X*_{poorʹ}

*S*_{rich} = 45 + 3*X*_{richʹ}

(a) Plot the above relationships and interpret the differences between the slopes and intercepts in intuitive terms. Do you think that the difference in the “productivity” of additional educational spending between rich and poor reflected in the above formulas is realistic? (To answer, you might focus on the differences in home life for the groups and differences in the availability of extra-curricular enrichment activities.)

(b) Derive and plot the community’s transformation curve between
*S*_{rich} and *S*_{poor},
remembering that *X*_{poor} and
*X*_{rich} must sum to 10. Because of the
linear relationship between *S* and *X* for each
group, the transformation curve is a straight line. (Hint: You
should be able to find the transformation curve solely by locating
its endpoints.)

(c) Find and plot the test scores that would result if the city divided the grant money equally between the schools.

(d) Find and plot the test scores that would result if the city allocated the grant money to equalize the scores across schools.

(e) Finally, consider the case in which the community’s goal is
to maximize its overall average test score, which equals
(*S*_{poor} + *S*_{rich}
)/2? How should it allocate the grant money? Find the answer by
using a diagram that extends the iso-crime line approach from the
chapter. (You will not get full credit for fi nding the answer by
trial-and-error number crunching, although you are welcome to
include such numbers along with your diagram). Using the results of
(a), explain why your answer comes out the way it does.

(f) What if the coefficient of *X*_{poor} in the
above formula had been equal to 2 and the coefficient of
*X*_{rich} had been equal to 1.5? Without
drawing any diagrams or doing any computations, you should be able
to tell how the community would allocate the grant money if its
goal were to maximize the average score. What allocation would it
choose?

(g) Suppose the community’s social welfare function is
(1/5)*S*_{poor} + √*S*_{rich}. How
should the grant money be allocated to maximize this function?
(here, you can crunch some numbers, or use calculus if you like).
Show the solution in your plot and contrast it to that from
(c).

Answer #1

Suppose that a city operates two neighborhood schools, one in
the rich neighborhood and one in the poor neighborhood. The schools
are equal in size and currently have equal budgets. The city
receives $10 million in federal grant money that can be used to
supplement the budgets of the two schools, which are initially
identical. For each school, the average score on a standardized
achievement test depends on how many dollars are allocated to the
school. Letting S denote the...

As Shaniq drinks additional cups of tea at breakfast,
Shaniq's
Question 1 options:
marginal utility from tea decreases.
total utility from tea increases.
total utility from tea decreases.
Both answers A and B are correct.
Both answers B and C are correct.
Question 2 (1 point)
You can use marginal utility theory to find the demand curve by
changing
Question 2 options:
only the price of one good.
only income.
only the prices of both goods.
the utility schedule.
Question...

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