The consumer faces non-negativity constraints

Assignment Help Business Economics

Reference no: EM131244388

Suppose that a consumer wants to maximize his happiness as expressed by utility function u(c1, c2). Her income is M and the prices of goods 1 and 2 are p1 and p2, respectively. The consumer faces non-negativity constraints.

1) Write down the problem of the consumer and the first order necessary conditions for c1* , c2∗ and λ∗ .Suppose that u(c1, c2) = log c1 + A log c2. Use the first-order conditions found above to find optimal c1∗ , c2∗ as functions of p1, p2 and M. (USE Kuhn-Tucker Theorem)

2) Now suppose that u(c1, c2) = log(c1) +c2. Also, suppose that the consumer faces prices and income (p1, p2, m) = (1, 5, 3). The consumer is faced with a budget constraint and two non-negativity constraints, one for each good. Solve for c1∗and c2∗. Hint: The utility function guarantees that the demand for one of the goods is strictly positive. What does this imply about its multiplier?

Reference no: EM131244388

Questions Cloud

The income elasticity of computers is positive : You hear that during the last recession in the early 1990s consumer incomes fell by 10% and the purchase of computers fell by 17%. From this you determine that: since the income elasticity of computers is positive, computers are a normal good

In nation with no inflation : In a nation with no inflation, the central bank raises the money supply by 6%, and each dollar is spent 1% more than it was before. From this we know:

Single supply and demand diagram representing one firm : Graph out this situation using a single supply and demand diagram representing one firm. Label the initial equilibrium price and quantity (P 1 , Q 1 ); Then demand increases, creating an excess demand. The firm can either respond by increasing price ..

Describe the economic principles that company executives : Describe the economic principles that company executives should consider when developing a strategy or strategies that will maximize profits while minimizing incentives for competitors to develop competing products.

The consumer faces non-negativity constraints : Suppose that a consumer wants to maximize his happiness as expressed by utility function u(c1, c2). Her income is M and the prices of goods 1 and 2 are p1 and p2, respectively. The consumer faces non-negativity constraints.

Planning to replace outdated equipment with models : A company is planning to replace outdated equipment with models that are more energy-efficient and environmental-friendly. Two models are under consideration. Model A is sold for $159,000 and can produce at an optimum speed of 78 units/hour. What ext..

Suppose the equilibrium price of oranges : Suppose the equilibrium price of oranges is .79, but government takes steps to prevent the price from exceeding .60. The likely result will be a:

Ethics in patient referrals act : This question relates to the Ethics in Patient Referrals Act, which is commonly referred to as the “Stark Law.” Under that law, which of the following statements, if any, is true?

Fortune magazine conducts an annual survey and publishes : Fortune magazine conducts an annual survey and publishes the rankings of the World's Most Admired Companies. Locate the most recent publicly available ranking, follow the link to the best companies, and focus on the nine factors highlighted by Fortun..

User Account

All Pages