📘 economics

1. The problem: Discuss two major critiques of Marx's Labor Theory of Value (LTV) and Marxist responses, then state which critique is most convincing and why. 2. Critique 1: Transf

1. **State the problem:** We are given demand and supply equations for maize and rice and need to find the equilibrium prices ($P_M$, $P_R$) and quantities ($Q_M$, $Q_R$). 2. **Equ

1. **State the problem:** We are given demand and supply functions for two commodities and need to find the equilibrium prices $p_1^*$, $p_2^*$ and quantities $Q_1^*$, $Q_2^*$ wher

1. **Problem:** Given the total-cost function $$C = Q^3 - 5Q^2 + 14Q + 75$$, write out the variable-cost (VC) function, find its derivative, and interpret the economic meaning of t

1. **State the problem:** We need to find the equilibrium prices $P_A$ and $P_B$ and quantities $Q_A$ and $Q_B$ where demand equals supply for both products A and B. 2. **Write dow

1. The problem is to find the marginal products $C^*$ and $L^#$ for the production function $$Q(C, L) = C^{\frac{1}{2}} \cdot L^{\frac{1}{2}}.$$ 2. The marginal product of input $C

1. **State the problem:** We need to visually construct the demand curve given the demand function $$P=4 \times Q + 100$$. 2. **Understand the demand function:** The demand functio

1. **問題陳述**： 我們有需求函數 $p(x) = x^2 + 16$ 和供給函數 $p(x) = -x^2 + 88$，其中 $x > 0$。

1. **Problem Statement:** Calculate the total area under the price-quantity curve for Customer A, which consists of an upper triangle, a rectangle, and a lower triangle, representi

1. **Menyatakan masalah:** Kita diberikan tabel produksi dengan variabel bibit (X), produksi total (Y), produksi rata-rata (Y/X), dan produksi marginal (\frac{\Delta Y}{\Delta X}).

1. **Problem Statement:** Find the equilibrium price and quantity for the commodity with supply function \(P_s = Q^2 + 6Q + 9\) and demand function \(P_d = Q^2 - 10Q + 25\). 2. **F

1. **Problem Statement:** We are given a 5% decrease in the price of chocolate sauce, which causes a 10% increase in the quantity demanded of chocolate sauce and a 15% increase in

1. **بيان المسألة:** عندما زاد دخل جودي من 130 إلى 170 في الأسبوع، زاد طلبها على تذاكر الحفلات بنسبة 15% وقلل طلبها على ركوب الحافلات بنسبة 10%.

1. **Problem Statement:** Judy's income increased from 130 to 170 per week. Her demand for concert tickets increased by 15%, and her demand for bus rides decreased by 10%. We need

1. Сформулюємо задачу: потрібно знайти мінімальне значення ціни $P$, при якому попит $Q(P) = 40 - 5P$ буде нейтральним. 2. Пояснимо, що означає "нейтральний" попит. Зазвичай нейтра

1. **Problem Statement:** We need to find the profit maximization for a steel firm producing $S$ units of steel and $x$ units of pollution.

1. **問題陳述**： 我們有需求函數 $p(x) = x^2 + 16$ 和供給函數 $p(x) = -x^2 + 88$，其中 $x > 0$。

1. **State the problem:** We are given the marginal revenue function $$MR(x) = 4x^3 - x^2 + 3x^2 - 4$$ (in hundreds of dollars) for selling $$x$$ hand-built bicycles. We need to fi

1. The problem involves verifying the equality \( \frac{MP_k}{P_k} = \frac{MP_l}{P_l} \) given the production function \( P = 12kl \) and marginal products \( MP_k = \frac{\partial

1. **State the problem:** Find the equilibrium price and quantity where demand equals supply. 2. **Given functions:**

1. A company finds that its profit $P(x)$ in thousands of dollars from producing $x$ units of a product is given by the quadratic function $$P(x) = -5x^2 + 300x - 2000.$$ Find the