A consumer has a utility function U (C₁, C₂) and her expenditure function is E = P₁C₁ + P₂C₂ where the prices of goods one and two are p₁ and p2 respectively. She wants to find the minimum level of expenditure, E* (P₁, P2, U), that allows her to achieve a certain level of utility U, i.e., so that U(C₁, C₂) ≥ U. Suppose that U(C₁, C₂) = (c₁)^(1/2)+ a(c₂)^(1/2) a) will constraint U(C₁, C₂) ≥ U bind. And what is the langranian for this problem B)Write down the Lagrangian conditions and find the ratio C1/C2 in terms a,p1or p2 C)Assume that a=1,p1 = pand p2 =1.Find C1 and C2. Substituting these values into the expenditure function, find E*(p, Ū), the minimum level of expenditure required to achieve the required level of utility Ū. Use this to prove that dE*/dp = C1
A consumer has a utility function U (C₁, C₂) and her expenditure function is
E = P₁C₁ + P₂C₂
where the prices of goods one and two are p₁ and p2 respectively. She wants to find the minimum level of expenditure, E* (P₁, P2, U), that allows her to achieve a certain level of utility U, i.e., so that
U(C₁, C₂) ≥ U.
Suppose that
U(C₁, C₂) = (c₁)^(1/2)+ a(c₂)^(1/2)
a) will constraint U(C₁, C₂) ≥ U bind. And what is the langranian for this problem
B)Write down the Lagrangian conditions and find the ratio C1/C2 in terms a,p1or p2
C)Assume that a=1,p1 = pand p2 =1.Find C1 and C2.
Substituting these values into the expenditure function, find E*(p, Ū), the minimum level of expenditure required to achieve the required level of utility Ū. Use this to prove that
dE*/dp = C1
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