Question #61313

Consider a representative consumer who is allocating her budget between housing and clothes. Her utility function is = . where is housing and is clothing. The price of housing is equal to 5 and the price of clothing is equal to 1. Initially the consumer starts out with a total budget M = 10.
A. Please state the consumers budget constraint.
B. Please find the consumers marginal utility of housing (MU#$) and his marginal utility of
clothing (MU%&)
C. Find the optimal consumption bundle of clothing and housing. Please show all the steps of your calculation (hint: use the condition ’()$ = ’()&).
*$ *&
D. Please find the optimal consumption bundle if the consumer total budget is 50
E. Use your answers from above to sketch the Engel curve for housing and clothing.
F. Is housing a normal or an inferior good for the representative consumer (base your answer on the Engel curve).

Expert's answer

A. The consumers budget constraint is 5Qh + 1Qc = 10.

B. The consumers marginal utility of housing and his marginal utility of clothing should be found as a derivative of the utility function, which is not given.

C. The optimal consumption bundle of clothing and housing should be found in the point, where MUh/Ph = MUc/Ph, MUh/5 = MUc/1 at the budget of M = 10.

D. The optimal consumption bundle if the consumer total budget is 50 will be found like in the part C.

The parts E and F can't be completed without the utility function.

B. The consumers marginal utility of housing and his marginal utility of clothing should be found as a derivative of the utility function, which is not given.

C. The optimal consumption bundle of clothing and housing should be found in the point, where MUh/Ph = MUc/Ph, MUh/5 = MUc/1 at the budget of M = 10.

D. The optimal consumption bundle if the consumer total budget is 50 will be found like in the part C.

The parts E and F can't be completed without the utility function.

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