Miguel and jake run a paper company. each week they need to produce 1,000 reams of paper to ship to their customers. the paper plant's long-run production function is q = 4k^0.75l^0.25 , where q is the number of reams produced, k is the quantity of capital rented, and l is the quantity of labor hired. for this production function, the mpl = k^0.75 / l^0.75 and the mpk = 3l^0.25 / k^0.25 . the weekly cost function for the paper plant is c = 10k + 2l, where c is the total weekly cost

a. what ratio of capital to labor minimizes jake and paul's total costs?

b. how much capital and labor will jake and paul need to rent and hire in order to produce 1,000 reams of paper each week?

c. how much will hiring these inputs cost them?

What do economists mean when they use the latin expression ceteris paribus?

For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. complete parts (a) through (c) below. x (cash prize, $) p(x) grand prizegrand prize 0.000000008860.00000000886 200,000 0.000000390.00000039 10,000 0.0000016950.000001695 100 0.0001582930.000158293 7 0.0039114060.003911406 4 0.0080465690.008046569 3 0.012865710.01286571 0 0.975015928140.97501592814 (a) if the grand prize is $13 comma 000 comma 00013,000,000, find and interpret the expected cash prize. if a ticket costs $1, what is your expected profit from one ticket? the expected cash prize is $nothing.

Instructions: use the following information to construct the 2000 balance sheet and income statement for carolina business machines. round all numbers to the nearest whole dollar. all numbers are in thousands of dollars. be sure to read the whole problem before you jump in and get started. at the end of 1999 the firm had $43,000 in gross fixed assets. in 2000 they purchased an additional $14,000 of fixed asset equipment. accumulated depreciation at the end of 1999 was $21,000. the depreciation expense in 2000 is $4,620. at the end of 2000 the firm had $3,000 in cash and $3,000 in accounts payable. in 2000 the firm extended a total of $9,000 in credit to a number of their customers in the form of accounts receivable. the firm generated $60,000 in sales revenue in 2000. their cost of goods sold was 60 percent of sales. they also incurred salaries and wages expense of $10,000. to date the firm has $1,000 in accrued salaries and wages. they borrowed $10,000 from their local bank to finance the $15,000 in inventory they now have on hand. the firm also has $7,120 invested in marketable securities. the firm currently has $20,000 in long-term debt outstanding and paid $2,000 in interest on their outstanding debt. over the firm's life, shareholders have put up $30,000. eighty percent of the shareholder's funds are in the form of retained earnings. the par value per share of carolina business machines stock is