Question

In: Economics

Consider a static (one-period), closed economy with one representative consumer, one representative firm, and a government....

Consider a static (one-period), closed economy with one representative consumer, one representative firm, and a government. The level of capital K and government expenditures G in the economy are both fixed exogenously. The government levies a lump sum tax T in order to fund its purchases, and the government budget must balance. Suppose the price of consumption is normalized to one (p = 1). The representative consumer has 24 hours of time available (h = 24), which she can use only for labor or leisure. She re- ceives labor income, profits from the firm (π), and pays lump sum taxes. The consumer’s utility function isu(c,l)=1/3 ln(c)+2/3 ln(l),andthefirm’sproductionfunctionisY =zKθN1−θ.

1. List the requirements that must be satisfied to achieve competitive equilibrium in this economy.

2.Suppose z=10,θ=1/4,K=96 and the wage is w=15 per hour of work. Solve the firm’s profit maximization problem for N∗. Compute the firm’s output Y and profit π at the optimal choice of N∗.

Solutions

Expert Solution

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Consider a two-period model of a closed economy with government. Assume that the representative agent is...
Consider a two-period model of a closed economy with government. Assume that the representative agent is endowed with ?1 and ?2 as initial endowments in period 1 and period 2 respectively, and has the utility function ? = ln ?1 + ? ln ?2, where ?1 and ?2 denote consumption and ? is the discount rate. Suppose that the government spends ?1 and ?2 in period 1 and period 2 and finances its expenditure through lump-sum taxes ?1and ?2 in...
Tax on labor income - Consider a one-period economy where the representative consumer has a utility...
Tax on labor income - Consider a one-period economy where the representative consumer has a utility function u(C;L) over consumption C and leisure L. Assume preferences satisfy the standard properties we assumed in class. The consumer has an endowment of one unit of time. She earns the wage w per unit of labor supplied to the market and has wealth A which yields an interest rate r, so her income is partly coming from labor, partly from capital. Suppose that...
Consider a one period economy in which the representative consumer has preferences over leisure (l) and...
Consider a one period economy in which the representative consumer has preferences over leisure (l) and consumption (c) described by the utility function u(c, l) = c0.5l0.5 This consumer has 1 unit of time h to spend between leisure, l, and labor supply, Ns. The representative firm’s production function is Y = zNd where Nd is labor demand and z = 2 is total factor productivity. The government buys one unit of consumption good, meaning that, G = 1. (a)...
Question 1. One period macroeconomic model We consider an economy closed to a period populated by...
Question 1. One period macroeconomic model We consider an economy closed to a period populated by consumers and produce. The representative consumer chooses the quantity of leisure, let of consumption, as its utility under budget constraint. The representative producer chooses the labor factor that maximizes his profile Preferences satisfy the same properties as in the standard consumer model Similarly, the production function, Y = F(K.N), where k is the capital stock and the quantum labor factor obeys the properties than...
Consider a one period macroeconomic model for the closed economy of the island of Anabel. Describe...
Consider a one period macroeconomic model for the closed economy of the island of Anabel. Describe the three agents in the model, the exogenous variables, and the endogenous variables in the model. Graph and describe the competitive equilibrium of Anabel's economy.
In the​ one-period model, education can be represented as time spent by the representative consumer that...
In the​ one-period model, education can be represented as time spent by the representative consumer that is neither leisure nor time applied to producing output. What the economy gains in the future is that the representative consumer then has more time​ available, as measured in terms of effective units of labour time​ (adjusted for skill​ level, or what economists call human​ capital). That​ is, the aggregate production function can be seen as Y=zF(K, eN)​, where e is the quantity of...
Consider a simple financial market for a closed economy with government, such as might be crudely...
Consider a simple financial market for a closed economy with government, such as might be crudely representative of the world as a whole. a) Construct a diagram to represent this market and note and explain your choice of the variables on the vertical and horizontal axes. b) Draw the saving supply curve and the investment demand curve, indicating and explaining which variables shift them to the right and left and why. c) Imagine that this market faces simultaneous pessimism shocks....
Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the...
Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible. Find the equation of an arbitrary indifference curve for this utility function (evaluated at ̅ utility level ?). Sketch of graph of this indifference curve (be sure to justify its shape and to derive/demark any points of intersection with the axes).
consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the...
consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible. Assume initially that ?? = ?? = 1 and ? = 10.  Derive the consumers equilibrium cross-price elasticity between goods ? and ? and evaluate the value of this elasticity at the initial parameter values given .
Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the...
Consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible. 1.a.Derive the consumer’s indirect utility function ?(∙). b.Then, derive the consumer’s expenditure function, e(∙), directly from ?(∙). c.Finally, derive the consumer’s Hicksian/compensated demand functions (denoted ? and ? , respectively) from e(∙). ?? 2.Assume initially that ?? = ?? = 1 and ? = 10....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT