Supply and Demand

In a free market economy, the price of a product is determined by the relationship between supply and demand. Suppliers are more willing to supply a product at higher prices. So when the price is high, supply is high. On the other hand, consumers of a product are generally less willing to buy a product at higher prices. So when the price is high, demand is low.

In a free competitive market, the price of a product tends to move toward an equilibrium price, in which the supply and demand are equal; that common value of the supply and demand is the equilibrium quantity. To find the equilibrium price, we solve the system consisting of the price-supply and price-demand equations.

Question 1

At a price of $4.82 per pound, the supply for cherries is 16,197 pounds, and the demand is 10,394 pounds. When the price drops to $4.15 per pound, the supply decreases to 10,868 pounds and the demand increases to 12,866 pounds. Assume that the price-supply and price-demand equations are linear.

What is the equilibrium price?

$ per pound. Round to the nearest cent.

Question 2

At a price of $4.86 per pound, the supply for cherries is 16,168 pounds, and the demand is 10,397 pounds. When the price drops to $4.17 per pound, the supply decreases to 10,923 pounds and the demand increases to 12,539 pounds. Assume that the price-supply and price-demand equations are linear.

What is the equilibrium quantity? Round to the nearest pound.

pounds.

Break-Even Analysis

Any manufacturing company has costs which include fixed costs such as plant overhead, product design, setup, and promotion; and variable costs that depend on the number of items produced. The revenue is the amount of money received from the sale of its product. The company breaks even if the revenue is equal to the cost.

Question 3

A small plant manufacturing riding mowers. The plant has fixed costs (leases, insurance, etc.) of $49,300 per day and variable costs (labor, materials, etc.) of $1,232 per mower produced. The mowers are sold for $1,958 each. The resulting cost and revenue equations are

y=y= 49,300 ++ 1,232 xx	Cost equation
y=y= 1,958 xx	Revenue equation

where xx is the total number of mowers produced and sold each day. The daily costs and revenue are in dollars.

How many mowers must be manufactured and sold each day for the company to break even?

mowers. Round to the nearest mower.

Question 4

A company manufactures dog leashes that sell for $18.48, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $23,200 and the variable costs (materials, shipping, etc.) are $6.8 per leash. How many leashes must be produced and sold each month for the company to break even?

leashes. Round to the nearest leash.

Corporate Income Tax

A corporation's taxable income is taxed at the federal, state, and local levels. It is customary for an agency to deduct the taxes paid to the other agencies before computing the company's tax liability. For example, the federal taxes are based on the income that remains after the state and local taxes are deducted. Similarly, the state taxes are based on the income that remains after federal and local taxes are deducted; the local taxes are based on the income that remains after state and federal taxes are deducted.

Question 5

A corporation has a taxable income of $7,325,957. At this income level, the federal income rate is 53%, the state tax rate is 22%, and the local tax rate is 8%. If each tax rate is applied to the the total taxable income, the resulting tax liability for the corporation would be (53 + 22 + 8)%. Luckily for the corporation, the taxes paid are deducted as described above. What is the tax liability (as a percentage of taxable income) if the customary deductions are taken into consideration?

%. Round to the nearest tenth of a percent (one decimal place).

Question 6

A corporation has a taxable income of $1,694,593. At this income level, the federal income rate is 47%, the state tax rate is 18%, and the local tax rate is 9%. If each tax rate is applied to the the total taxable income, the company would have to pay $1,694,593 * 0.47 in federal taxes. Luckily for the corporation, the taxes paid are deducted as described above. How much is paid in federal taxes if the customary deductions are taken into consideration?

$ . Round to the nearest dollar.

Question 7

A corporation has a taxable income of $2,560,134. At this income level, the federal income rate is 55%, the state tax rate is 23%, and the local tax rate is 10%. If each tax rate is applied to the the total taxable income, the company would have to pay $2,560,134 * 0.10 in local taxes. Luckily for the corporation, the taxes paid are deducted as described above. How much is paid in local taxes if the customary deductions are taken into consideration?

$ . Round to the nearest dollar.

Delivery Charges

Many package delivery services charge a base price for packages up to some weight and a surcharge for each additional pound (or fraction thereof).

Question 8

Jesaki Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $25.08 for shipping a 6.3 pound package and $65.83 for shipping a 22.1 pound package. What is the base price that Jesaki Express charges for packages weighing 1 or less?

$ . Round to the nearest cent.

Question 9

Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $29.05 for shipping a 6.4 pound package and $64.61 for shipping a 18.4 pound package. What is the surcharge that Yaster Shipping charges for each additional pound (or fraction thereof) beyond 2 pounds?

$ per pound above 2 pounds. Round to the nearest cent.

Question 10

Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 1 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $31.2 for shipping a 6.1 pound package and $64.22 for shipping a 19.1 pound package. How much does it cost to ship a 31.8 pound package?

$ . Round to the nearest cent.