Homework Answers
1.
Here car and tyres are complementary goods because they are always use together in a fixed proportion. So utility function for perfect complement:
U(C, T)= Min [C, (1/4) T]
C= Quantity of car
T= quantity of tyres
They are used in fixed proportion,So:
C = (1/4)T
4C = T Equation 1
Budget line: Cx + Ty = M
Use the equation 1 in budget line: Cx + 4Cy= M
C(x+4y)= M
C= M/(x+4y) Utility maximization quantity of Car
Use this in equation 1:
4 [M/(x+4y)] = T Utility maximization quantity of Tyre
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Suppose a person has a utility function U(x1,x2)= xa1+xa2, which she maximizes subject to her budget...
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which
she maximizes subject to her budget constraint, px1 + qx2 = m,
where p, q, m are all positive. Use the Lagrangian method to solve
the maximization problem, and find the demand functions for the
consumer. Show that the demand functions are homogeneous of degree
zero in prices (p, q) and income (m)
(2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y...
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2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer Utility Function C1...
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1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y}...
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l. (a) "Utility maximization is achieved when the budget is allocated so that the marginal utility per euro of expenditure is the same for each good". Explain this statement. A consumer has є100 of income to allocate between bread and pizzas. Bread costs €1 per loaf. (b) Suppose when pizza costs €5 per unit, the consumer chooses 10 pizzas. Draw the budget constraint and the indifference curve to represent this budget and choice. Be specific about where the budget line...
1. Consider the utility maximization problem maxx+a Iny s.l. px + 4y = m, where 0 <a<m/p. (a) Find the solution (** y*). (b) Find the indirect utility function U*p,,m,a), and compute its partial derivatives wrtp, m, and a (c) Verify the envelope theorem.
Suppose a person has a utility function U(x1,x2)= xa1+xa2, which
she maximizes subject to her budget constraint, px1 + qx2 = m,
where p, q, m are all positive. Use the Lagrangian method to solve
the maximization problem, and find the demand functions for the
consumer. Show that the demand functions are homogeneous of degree
zero in prices (p, q) and income (m)
(2.5 marks) Suppose a person has a utility function U(x1, x2) = xq +xm, which she maximizes...
M 4. Consider the utility maximization problem max U(x,y) = x +y s.t. x + 4y = 100. (a) Using the Lagrange method, find the quantities demanded of the two goods. (b) Suppose income increases from 100 to 101. What is the exact increase in the optimal value of U(x, y)? Compare with the value found in (a) for the Lagrange multiplier. (C) Suppose we change the budget constraint to px + y = m, but keep the same utility...
1. Suppose a consumer has the utility function over goods x and y u(x,y) = 3x{y} (a) Setup the utility maximization problem for this consumer using the general budget con- straint. (2 points) (b) Will the constraint be active/binding? Is the sufficient condition for interior solution satisfied? Prove your answers. (4 points) (c) Solve the utility maximization problem for the Marshallian demand equations x* (Px. Py,m) and y* (Px.p.m). Show all of your work and circle your final answers. (7...
1. Solve the maximization problem: mary = 29.252.0,75 s.t.100 – 2.11 - 4.02 = 0 (1) 2. Suppose that Jeff cares only about basketball (B) and football (F). His utility function is U = B04F0.6The price of a basketball ticket is $5, and the price of a football ticket is $10. Jeff has a budget of $100. What is the solution to Bruce's maximization problem? 3. Find level set and tangent line at (1,1) of the function: y = x...
1. Solve the maximization problem: maxy = 20,25,975 s.t.100 - 201 - 4x2 = 0 (1) 2. Suppose that Jeff cares only about basketball (B) and football (F). His utility function is U =B04F06 The price of a basketball ticket is $5, and the price of a football ticket is $10. Jeff has a budget of $100. What is the solution to Bruce's maximization problem? 3. Find level set and tangent line at (1,1) of the function: y = x...
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