Microeconomics: Consumer Theory and Production Theory

Production Theory

• Production theory is the opposite of consumer choice theory.

Consumer Theory

• The objective function is to maximize utility (Uc) subject to a budget constraint.
• The utility function is explained by an indifference curve.
• The marginal rate of substitution (MRS) is the rate at which one good is substituted for another while keeping the level of utility constant.

Theory of a Firm

• The objective is to maximize profit (π) by finding the optimal output (q) given the production function q = f(L, K).
• The production function is explained by isoquants.
• The marginal rate of technical substitution (MRTS) is the rate at which one input is substituted for another while keeping the output constant.

Cost Curves

• Total cost (TC) is the sum of fixed cost (FC) and variable cost.
• The variable cost is the total expenditure on labor (wL) and capital (Kr).
• The cost curves are derived from the production function and the cost of inputs.

Revenue, Variable, and Average Cost

• Revenue is the total amount of money earned by a business from selling its goods or services.
• Marginal revenue is the additional revenue earned by selling one more unit of the good or service.

Aggregate

• The aggregate is a measure of the total output of a firm or industry.
• It is affected by the level of inputs and the production function.

Economic Concepts

• Profit-maximizing output is the level of output where the marginal cost of production equals the marginal revenue.
• Law of diminishing marginal product: the marginal product of an input decreases as the input increases.
• Technical efficiency: the optimal combination of inputs to produce a given output.

Production Function

• A production function is a mathematical function that describes the relationship between inputs and outputs.
• The properties of a production function include:
  • It is never empty.
  • It is increasing in inputs (f'(x) > 0).
  • It is universally hyperexponential.

Exercise

• The exercise is to find the rate of change of output when an additional unit of labor is employed, given a production function.
• The answer is found by taking the derivative of the production function with respect to the input.

Properties of Production Functions

• If the production function is strictly increasing, then the marginal product (MP) is positive.
• If the production function is additively depreciable, then the marginal product is negative.

Demand and Supply

• Demand is the quantified product that customers want and are ready to buy at a given price.
• Supply is the quantified product that producers want and are ready to sell at a given price.
• The assumptions of demand and supply analysis include:
  • The assumption that everything else remains the same.
  • The demand and supply curves can be represented by a shift in the curve.

Key Concepts

• Demand schedule: a table showing the quantity demanded at different prices.
• Demand curve: a graphical representation of the demand schedule.
• Supply schedule: a table showing the quantity supplied at different prices.
• Supply curve: a graphical representation of the supply schedule.
• Market equilibrium: the point at which the demand and supply curves intersect.
• Consumer and producer surplus: the difference between the willingness to pay and the market price, and the difference between the market price and the willingness to accept.

Mathematical Equations

• The equation for quantity demanded is Qd = 20 - P/2, and for quantity supplied is Qs = P/2 - 5.
• The equilibrium price and quantity are found by solving the equation Qd = Qs.

Isoquants and MRTS

• Isoquants are curves that show the alternative combinations of inputs that can be used to produce a given level of output.
• The marginal rate of technical substitution (MRTS) is the rate at which one input is substituted for another while keeping the output constant.
• The MRTS is calculated as the ratio of the change in the input on the y-axis to the change in the input on the x-axis.

Properties of Isoquants

• Isoquants are negatively sloped.
• Isoquants cannot cross.
• Isoquants are convex to the origin.
• The higher the isoquant, the higher the output on the isoquant curve.

Feedback Control

• Feedback control is a system that uses output equations to invent its own behavior.
• The system responds to a step input by adjusting its output to reduce the difference between the actual and desired values.

The System Response

• The system's response to a step input is determined by its dominant pole.
• If the pole is complex, the system will oscillate before stabilizing.
• If the pole is real, the system will smoothly approach the steady-state value.

The Feedback Gain

• The feedback gain is a critical factor in the behavior of a system.
• The gain can be changed in various places.

The System's Response to a Step Input

• The system's response to a step input is affected by the output change that occurs because of the step input.
• The system's ability to respond is determined by the location of the system's poles on the poles and zeros map.