Question

Over the past decade, medical costs have increased more rapidly than other prices. In order to illustrate how rising medical costs have affected consumer alternatives, let X represent the number of medical services, and let Y represent the number of other goods. Furthermore, let income (M) be measured in hundreds of dollars, the price of medical services and other goods in terms of dollars per minute, with M = 100, Px = 4, and Py = 5.
a. Graph the budget line, and determine the market rate of substitution.
b. Illustrate the budget set.
c. Show in your graph what happens to the budget constraint if Px increases to $10.
d. What is the meaning of the slope of the two budget constraints?

Answer 1

Answer:

Budget Line is the graphical representation of goods combinations, which a consumer can buy - given prices & income (spending all income)

Equation : X.Px + Y.Py = M

{where X & Y are quantities of goods X & Y ; Px & Py are prices of goods X & Y}

a. Putting price of : X= medical services ; Y = other goods ; M = 100 :-

Budget Line : 4X + 5Y = 100

Budget Set represents good combinations, which a consumer can get - given prices & income (not necessarily spending all income)

Equation : X.Px + Y.Py ≤ M.  All the area below Budget Line is Budget Set.

b. Market rate of substitution is the slope of budget line which is equal to price ratio of the goods i.e Px/Py = 4/5 = 0.8

c. Increase in Px: reduces the intercept of the axis representing Good X consumption & rotates the curve inwards on that axis. As - less of that good can be consumed with same income, due to price rise.

d. Slope of Budget Constraint: is price ratio of the two goods (Px/Py), as it denotes the amount of a good needed to be sacrifised for gaining an additional unit of the other good.