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Suppose that a consumer is consuming banana and hazelnut
Suppose that a consumer is consuming banana and hazelnut. Price of banana is 5TL, while the price of hazelnut is 10 TL. The consumer's income is 100 TL. Marginal rate of subsitution between banana and hazelnut is given as follows: MU QF MRSFM MU OM a) Write the equation of the budget line. b) Calculate the slope of the budget line. c) Obtain the equilibrium quantity of banana and hazelnut for the consumer. Show equilibrium point on the graph. d) Suppose that the income of the household doubles. If the hazelnut is an inferior good for the consumer, what will be the possible equilibrium point? Show on the graph.
Expert Solution
a)The equation of budget line is given as :
M? = px.x + py.y
M= 100
Px= 5
Py = 10
100= 5Qf+ 10Qm
Qf= banana
Qm = Hazelnut
b)Slope of budget line is given by : -px/py
= -5/10
c)MRS???mf=-Qf/Qm
The consumer equilibrium point is given by :
MRSxy = MUx/MUy = Px/Py
Qf/Qm= 1/2
2Qf= Qm ( equation 1)
100= 5Qf+ 10Qm
Putting the value of Qm from equation 1
100= 5Qf + 20Qf
100= 25Qm
Qm=4
Qf=2
d)Inferior good is a good whose consumption falls with increase in income. The possible equilibrium would have Qm less than 4 and Qf greater than 2.
Assume X denotes hazelnut and Y denote banana. When income doubles the budget line shifts outward. Initially the consumer is at 11 and equilibrium point is at (X1,Y1). Since X is an inferior good .It's consumption would fall after increase in income. The final equilibrium would be at ( X2, Y2)
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