Answer:
Optimal number of donuts = 5 Donuts
Optimal cups of coffee = 2.5 cups.
Explanation:
Optimal numbers of donuts and coffee can be calculated as follow
First, we need to determine the budget constraint as below
M = ( P(D) x D ) + ( P(C) x C )
Placig values in the formula
10 = D + 2C
Now make utility function as:
U(D,C) = D0.5 C0.5
Marginal Utility donuts
MU(D) = 0.5D-0.5C0.5
Marginal Utility Coffee
MU(C) = 0.5D0.5C-0.5
The formula for marginal rate of substitution
(MRSD,C)= MU(D) / MU(C) = 0.5D - 0.5C0.5 / 0.5D0.5C - 0.5 = C/D
Now calculate the optimal consumption level
MRSD,C = P(D) / P(C)
C/D = 1/2
D = 2C (Equation 1
)
Placing the value of D resulted from equation 1, in the budget constraint we as below
10 = D + 2C
10 = 2C + 2C
10 = 4C
C = 10/4 = 2.5
NOw place the value of C in equation 1
D = 2C = 2(2.5) = 5
Optimal number of donuts = 5 Donuts
Optimal cups of coffee = 2.5 cups.
