The demand function is typically expressed as 
q = f(p). 
What does the variable q represent?

Q represents the quantity demanded of a commodity.

Fill in the blank: The slope of the demand curve is ___, indicating that price and quantity demanded are ___ related.

Negative; inversely

True or False: The supply function is defined as x = f(p) where x is the amount offered and p is the price.

True

What is the formula for marginal cost if C(x) is the total cost function?

Marginal cost is given by C'(x), which is the derivative of the total cost function with respect to output x.

If R(x) denotes total revenue, what is the relationship between R(x) and marginal revenue?

Marginal revenue is the derivative R'(x), representing the additional revenue gained from selling one more unit.

Fill in the blank: The price at which quantity demanded equals quantity supplied is called the ___ price.

Equilibrium

Calculate the equilibrium price if the demand function is Qd = 4 - 0.06p and the supply function is Qs = 0.6 + 0.11p.

Equilibrium price is 20.

What does the elasticity of demand measure?

The elasticity of demand measures the responsiveness of quantity demanded to a change in price.

If the demand function is q = 100 - p - p², find the elasticity of demand when p = 5.

Elasticity of demand is 2.5.

True or False: The elasticity of supply is defined as the ratio of the relative change in quantity supplied to the relative change in price.

True

Given the cost function C(x) = (1/10)x³ - 4x² + 20x + 5, find the average cost when producing x units.

Average cost is (1/10)
x² - 4x + 20 + (5/x).

Fill in the blank: The relationship between marginal revenue and elasticity of demand is expressed as MR = ___.

AR(1 - 1/ε), where AR is average revenue and ε is the elasticity of demand.

What is the formula to calculate average variable cost (AVC) from total cost?

Average variable cost is calculated as AVC = f(x)/x, where f(x) is the variable cost function.

Calculate the total cost when output is 10 units if the total cost function is given by C(x) = 1/10 x³ - 4x² + 20x + 5.

C(10) = 1/10(10)³ - 4(10)² + 20(10) + 5 
= 100 - 400 + 200 + 5 
= -95.