Please show work with steps Douglas\'s utility function for restaurant meals (R)
ID: 1176852 • Letter: P
Question
Please show work with steps
Douglas's utility function for restaurant meals (R) and home-cooked meals (H) is: U = 12 R + 4 H Suppose Douglas has a monthly food budget of Y = $270. Restaurant meals cost $9, and home-cooked meals cost $5. Sketch his budget constraint with R on the X axis and H on the Y axis. What is the MRT (slope of the budget constraint)? What is Douglas's MRS ? (How many home meals is he willing to give up, to get one more R?) Are these goods complements, substitutes, or perfect substitutes? What is his optimal consumption bundle? Show this point on our graph. Later, the price of home cooked meals changed, such that Douglas decided to consume some R and some H during the same month. What must the new price of H be for this to occur? (Assuming Pr still is $9).Explanation / Answer
The budget constraint line should have the equation:
9R + 5H = 270
Plotting this on the grph we get the slope to be:
MRT = 54/30 = 9/5
Now, since this is a linear consumption function MRS = MRT
So, For an extra R meal, doughlas has to give up 9/5 = 1.8 meals of H
So, for one increase in R meal, utils go up by 12 and come down by (4*1.8 = 7.2 utils)
His optimal budget consumption would be when the utility would be maximum.
This would occur when R = 30 and H = 0
Utitilty = 12 * 30 = 360 utils
For Doughlas to consume both in the same month, the price of Home cooked meals must fall so that more H is avaliable.
This would be possible if H meals provide atleast the same utility to Doughlas as the R meals.
So,
360 utils / 4 = 90 meals
So, 90 H meals should be possible within $270
Hence new price should be : 270 / 90 = $3 per Home cooked meal.
Thus, R meal and H meal would become perfect substitutes.
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