Question

Jane's income is $500 a semester. The price of one day of skiing per semester is $100, and the price of one day of horseback riding is also $100. The figure shows Jane's preference map for days of skiing and horse back riding per semester.

7 4 3 Curve B Curve A Curve C 0 2 3 567 6 Days of horseback riding per semester

What quantities of days of skiing and days of horseback riding does Jane buy? What is Jane's marginal rate of substitution at the point at which she consumes?

Suppose that the price of one day of horseback riding rises to $150 and the price of one day skiing and Jane's income remain the same. What quantities of days of horseback riding and days of skiing does Jane now buy? What are two points on Jane's demand curve for days of horseback riding?

Draw Jane's demand curve of horseback riding

.

Suppose that the price of one day of horseback riding rises to $150 and the price of one day skiing and Jane's income remain the same.

What is the substitution effect of this price change and what is the income effect of the price change?

Is one day of horseback riding a normal good or an inferior good? Explain.

How would a production function that exhibits decreasing marginal product affect the shape of the total cost curve? Explain or draw a graph.

What effect, if any, does diminishing marginal product have on the shape of the marginal cost curve?

Answer 1

Consider the given problem here there are two goods “house riding” and “skiing”. Now, the consumer has “$500” and the price of each of the goods is “$100”, => “A1B1” be the budget line is this case. Consider the following fig.

So, here “X” be the optimum point where “IC” is tangent to “Curve A” and the budget line “A1B1”. So, here optimum consumption choice is given by “X=3, Y=2”. Now, here the indifference curve “A” is tangent to the budget line, => “MRS = price ratio = 100/100 = 1”, => at the optimum “MRS = 1”.

Now, let’s assume that the price “house riding” increases to “150”, => the budget line get steeper, => the new budget line is given by “A1B2” with absolute slope “150/100 = 1.5”. Now, the new equilibrium point is given by “T” the tangency point between “A1B2” and the indifference curve “C”. So, here the optimum consumption is given by “X=2, Y=2”. So, here the price of “house riding” increases implied the consumption of it decreases to “2”.

Consider the following of the demand for “horse riding”.

So, here there two pints “E1” where “P=100, X=3” and “E2” where “P=150, X=2”. So, here the demand curve is downward sloping.

Now, to decompose the “total effect of price change” into “SE” and “IE”, we have to draw a budget line parallel to”A1B2” but is tangent to the indifference curve “A”. So, here the equilibrium point is “C”. So, here the movement from “T” to “C” shows the “SE” and the movement from “C” to “X” shows the “IE”.

Now, if we draw another budget line “A3B4” which parallel to “A2B3”, => the new budget line shows the higher level of income compare to “A2B3”. So, here the optimum consumption bundle is given by “D”. So, here point “D” shows lower of “X” compare to “C”, => the consumption of “X” decreases for a sufficiently larger level of income, => “horse riding become inferior” for larger level of income.