Question
In: Economics
Consider a consumer with the Utility function: U = C^1/5 O^ 4/5 and facing a budget...
Consider a consumer with the Utility function: U = C^1/5 O^ 4/5 and facing a budget constraint: M ≥ PcC +PoO
Note: For this utility function MUC = (1/5)C^-4/5 O^ 4/5 and MUo = (4/5)C^1/5 O^ -1/5 Where C denotes the consumption of corn, and O denotes the consumption of other goods.
A) Derive the Marshallian demand functions for C and O using the equilibrium conditions for an interior solution.
B) Graph and fully label the Demand Curve for corn if income is M=100. To do this, solve for demand when the price of corn is 10, 20, and 40, then approximate the demand curve using these three points.
Solutions
Expert Solution
(a) U = C^1/5 O^ 4/5
MUC = (1/5)C^-4/5 O^ 4/5
MUo = (4/5)C^1/5 O^ -1/5
At equilibrium condition (or utility maximization point), (MUc / MUo) = (Pc / Po)
=> [(1/5)C^-4/5 O^ 4/5 / (4/5)C^1/5 O^ -1/5] = (Pc / Po)
=> [(1/4) O^4/5 * O^1/5 / C^1/5 C^4/5] = (Pc / Po)
=>1/4 (O/C) = (Pc / Po)
=> O = 4C*(Pc / Po) ---------------(1)
---------
Budget constraint: M ≥ PcC +PoO
=> M = PcC +PoO
Put eq(1)
=> M = Pc*C +Po*O
=> M = Pc*C + Po* [4C(Pc/Po)]
=> M = Pc*C + 4C*Pc
=> M = 5C*Pc
=> C = (M/5Pc) ---------------- Marshaliian demand function for C.
Put Marshallian demand function for C in eq (1)
O = 4C(Pc/Po)
> O = 4 * (M/5Pc) (Pc/Po)
=> O = (4/5) (M/Po) -------------------- Marshallian demand function of O
------------------------------------------------------------------------------------------------------------------
(b) C = (M/5Pc)
Put M = 100
=> C = (100 / 5Pc)
=> C = (20 / Pc)
| Price of corn (Pc) | Demand for corn (C) |
| 10 | 2 |
| 20 | 1 |
| 40 | 0.5 |
----------------------------------------------
----------------------------------------------------
Rahul Sunny answered 1 year agoRelated Solutions
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