Warren has $144 to spend on hamburgers (h) and gelato (g). His utility function is u(h,g)=2√hg+10. Hamburgers cost pH= $4 and gelato costs pG= $4. (i) Find Warren's optimal bundle. (ii) Now suppose the government imposes a $5 unit tax on hamburgers, which raises the price to $9.What is Warren's optimal bundle now? (iii) Finally, suppose that the government gives Warrena lump-sum subsidy of $72 while still imposing the tax. What is Warren's optimal bundle inthis case? (iv) Suppose that the government had simply imposed the tax (without a subsidy).Use the answers from(i) –(iii) to find the substitution and income effects from the increase in the price of hamburger
Warren has $144 to spend on hamburgers (h) and gelato (g). His utility function is u(h,g)=2√hg+10. Hamburgers cost pH= $4 and gelato costs pG= $4.
(i) Find Warren's optimal bundle.
(ii) Now suppose the government imposes a $5 unit tax on hamburgers, which raises the price to $9.What is Warren's optimal bundle now?
(iii) Finally, suppose that the government gives Warrena lump-sum subsidy of $72 while still imposing the tax. What is Warren's optimal bundle inthis case?
(iv) Suppose that the government had simply imposed the tax (without a subsidy).Use the answers from(i) –(iii) to find the substitution and income effects from the increase in the price of hamburger.
Two goods: hamburgers (h) and gelato (g)
Price: Ph=$4 and Pg=$4
u(h,g)=2√hg+10
Money Income(M)=$144
(i) For optimality, we require the following condition to be satisfied:
Marginal utility per rupee of both the goods must be equal, i.e,
MUh/Ph=MUg/Pg
MU is the marginal utility. It is derived by taking the first-order derivative of the utility function. It is the utility gained when an additional unit of the good is consumed.
MUh=2(0.5)(g/h)^0.5=(g/h)^0.5
MUg=2(0.5)(h/g)^0.5=(h/g)^0.5
Putting this in the above equation;
[(g/h)^0.5]/4=[(h/g)^0.5]/4
h=g
Putting this in the budget constraint:
Budget constraint; Ph.h+Pg.g=M
4h+4h=144
8h=144
h*=18
g*18
Optimal bundle=(18,18)
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