Please answer the following question typed. 1. Consider a firm aiming to maximising total profits from time 0 through infinity. The firm'sproduction function is f(k,) where k, is the capital stock at time t. New investment is i,, andcosts w;-00maxt=0s.t. kr41 = (1 - 8)k, + i,.Solve for the condition that determines the firm's optimal investment decision given k,.

As per the question, we aim to determine the condition that governs a firm's optimal investment…

Answered: Consider a firm aiming to maximising…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the supply of labor is N=1000 + 1000w. Find the market clearing real wage rate and level of employment. What happens to the wage rate and employment if wealth rises, reducing the supply of labor to N= 500 + 1000w? As in (a), what is the unemployment rate if real wage is 1 more than the equilibrium wage? (hint: solve the real wage and then add it by 1, then find the difference of quantity of labor supplied and demanded).
A fixed cost of $50 thousand was incurred in setting up an operation. At time t months thereafter, the operation yields income at the rate of (20 - 0.3t) and incurs expense at the rate of (10 - 0.1t), where both rates are in thousands of dollars per month. What is the optimal time to terminate the operation? What will total profit be at the optimal time of termination?
Given two inputs X1 and X2 with prices W1 and W2 respectively and a production function Y=f(X1,X2), show that cost minimisation implies that the marginal rate of substitution between the inputs X1 and X2 is equal to the ratio of the two inputs prices
Suppose that Marie produces milk q using her own labor l and cattle k using the production functionq = f(k, l) = k2/3ℓ1/3Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. a) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P). b) Now consider Marie’s problem in the long run, where her stock of cattle may vary. Set up her long run cost minimization problem and find her labor ℓc(q) and capital kc(q) demands and cost function C(q). c) Set up Marie’s long run profit maximization problem and find her long run supply curve q(P).
Suppose that in a certain market the demand function for a product is given by 10p + q = 2,100 and the supply function is given by 50p − q = 1,250. (Assume the price is measured in dollars.) If the government levies a tax of $5 per item, find the equilibrium point after the tax is levied. The tax is added to the selling price of the product.
find the consumers surplus if the demand function for a particular beverage is given by D(q)=(3000)/((3q+2)^(2)) and if the supply and demand are in equilibrium at q=5
Consider a Kenyan labor market with the following demand and supply functions respectively: QD = 200 – W AND and QS = 120 + W; 4- in; where QD is quantity of labour demanded; QD is quantity of labor supplied and w• is the wage rate is USD in the market.Suppose the Kenya government introduces a minimum wage of USD 100 in this market, calculate the unemployment rate caused by the minimum wage in the economy
Suppose that in a certain market the demand function for a product is given by 10p + q = 2,100 and the supply function is given by 50p − q = 1,250. (Assume price is measured in dollars.) If the government levies a tax of $5 per item, find the equilibrium point after the tax is levied. The tax is added to the selling price of the product. (q, p) =
The consumer demand curve for Professor Stefan Schwarzenegger’s dumbbells isgiven by q = (118 − 2p)^2 where p is the price per dumbbell, and q is the demandin weekly sales. Find the price Professor Schwarzenegger should charge for his dumbbells to maximize revenue. (Round your answer to the nearest cent.)

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