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Kumar spends all his monthly income of $20 on two goods, rice (x) and cooking oil (y). The price of oil is $1 per liter. Rice can be purchased at a government-run store and also on the free market. The price of rice is $1 per kilogram at the government store but he can only buy up to 10 kgs. In the free market, the price of rice is $2 per kg. Draw Kumar’s budget constraint assuming that the goods are divisible.
3. X Company is evaluating its cost of capital under alternative financing arrangements. In consultation with investment bankers, X Company expects to be able to issue new debt at par with a coupon rate of 10% and to issue new preferred stock with a $4.00 per share dividend at $25 a share. The common stock of X Company is currently selling for $20.00 a share. X Company expects to pay a dividend of $2.50 per share next year. Market analysts foresee a growth in dividends in Invest stock at a rate of 5% per year. Invest does not expect its cost of debt, preferred stock or common stock, to be different under the two possible financing arrangements. X Company marginal tax rate is 40%. Hint: coupon rate of the bond is the same as the before-tax cost of debt. The two arrangements are: Financing Arrangement, Debt, Preferred Stock, Common Stock, respectively
1, 20% 30% 50%& 2, 50% 30% 20%
B. What is the weighted average cost of capital to X Company under the second financing arrangement?
Find derivatives of the following functions:
• y=(4x+3)/ln[2x2 +3x−5] • y=3(e2x +e−2x)(x2 −4)
The following is the condensed information from the records of Hilal Manufacturing Company for the month of December 2021.
5000 units in process December 01, 2021 (40% Completed to material & 60% to CC)Rs. 30,000
Cost incurred during December
Direct MaterialRs. 74,000
LaborRs. 57,600
Applied FOHRs. 43,200
The Company has started 13,000 units in December 2021. There are 3000 units in process at the end of month which is 60% completed to material and 80% completed to CC.
Required:
Prepare cost of production report of the company for the month of December 2021 using FIFO method.
here are 5,000 identical individuals in the market of commodity X, each with a demand function given by Qdx = 6 - P, and 1,000 identical producers of commodity X, each with a function given by Qsx = 10P, where Qdx is an individual's quantity demanded, Qsx is a single producer's quantity supplied, and Px is the price of the commodity.
a. Find the market demand function (QDx) and the market supply function (QSx) for commodity X.
b. Determine the market demand schedule and the market supply schedule of commodity X (for whole dollar prices) and from them find the equilibrium price and the equilibrium quantity.
c. Plot, on one set of axes, the market demand curve and the market supply curve for commodity X and show the equilibrium point.
d. Obtain the equilibrium price and the equilibrium quantity mathematically.
e. Explain why the equilibrium condition is considered stable.
f. Determine the elasticity of demand for commodity X at the equilibrium point.
6. Find the maximum and minimum values of the following functions
a) 3X4 -X3 +2
b) x4 – 14x2 +24x +9
7. Find the profit maximizing output given Q = 200 – 10p and AC = 10 + Q25 where Q is quantity, p is price and AC is average cost.
8. Find the first order and second order partial derivatives of the following function
a) Z = 2x3 +5 x2y +xy2 +y3
b) Z = log (x2 + y2)
9. Find elasticity of demand if demand function is x = 250 – 5p +p2. Also find elasticity of demand at p = 8
10. Find elasticity of demand if demand function is p = 50 – 3q. Also find elasticity of demand at p = 5
Suppose that the manager of a firm is planning to meet an order of 1000 units of two products X and Y. The manager's problem is to find the combination of two goods that minimize its cost. He has the firm's cost function of two goods estimated as
C = 5X2 + 20 Y2
By using the Lagrangian multiplier method, find the quantity of X and quantity of Y, subject to X + Y = 1000, that minimize the cost of meeting the order.
A company produces two goods X and Y. The profit function of the company is given as follows:
P = I00X- 2X2 - XY + 180Y – 4Y2
The company is under obligation to produce a minimum combined output of 30 units. Find the output of X and Y subject to a total of 30 units that maximize total profit by using Lagrangian multiplier methods.
Suppose a firm has its TR and TC functions estimated as follows:
TR = 300Q-3Q2
TC = 500 + 50Q + 2Q2
Find (a) profit function of the firm, (b) the quantity of output (Q) that maximizes the firm's profit.
A manufacturer in a monopolistically competitive industry produces two different brands of a product for which the demand functions are P1=56-4Q1 and P2=48-2Q2. and the joint cost function is
TC=Q12+5Q1Q2+Q22. Find the profit maximizing level of output and the price that should be charged for each brand.
